linear_algebra.finsupp
⟷
Mathlib.LinearAlgebra.Finsupp
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
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(last sync)
Move map_finset_sup
/map_finset_inf
from order.hom.lattice
to data.finset.lattice
. This breaks a few unqualified downstream uses of submodule.map_bot
.
@@ -260,7 +260,7 @@ begin
haveI := classical.dec_pred (λ x, x ∈ (⋃ i, s i)),
suffices : ((submodule.subtype _).comp (restrict_dom M R (⋃ i, s i))).range ≤
⨆ i, supported M R (s i),
- { rwa [linear_map.range_comp, range_restrict_dom, map_top, range_subtype] at this },
+ { rwa [linear_map.range_comp, range_restrict_dom, submodule.map_top, range_subtype] at this },
rw [range_le_iff_comap, eq_top_iff],
rintro l ⟨⟩,
apply finsupp.induction l, { exact zero_mem _ },
@@ -633,7 +633,8 @@ variables {α} {M} {v}
theorem total_on_range (s : set α) : (finsupp.total_on α M R v s).range = ⊤ :=
begin
rw [finsupp.total_on, linear_map.range_eq_map, linear_map.map_cod_restrict,
- ← linear_map.range_le_iff_comap, range_subtype, map_top, linear_map.range_comp, range_subtype],
+ ← linear_map.range_le_iff_comap, range_subtype, submodule.map_top, linear_map.range_comp,
+ range_subtype],
exact (span_image_eq_map_total _ _).le
end
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Given a $k$-linear $G$-representation $A,$ this defines the $k$-linear isomorphism between functions $G^n \to A$ and representation morphisms $Hom(k[G^{n + 1}], A),$ called Rep.diagonal_hom_equiv
.
Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr>
@@ -344,7 +344,7 @@ theorem lsum_symm_apply (f : (α →₀ M) →ₗ[R] N) (x : α) :
end lsum
section
-variables (M) (R) (X : Type*)
+variables (M) (R) (X : Type*) (S) [module S M] [smul_comm_class R S M]
/--
A slight rearrangement from `lsum` gives us
@@ -362,6 +362,24 @@ lemma lift_apply (f) (g) :
((lift M R X) f) g = g.sum (λ x r, r • f x) :=
rfl
+/-- Given compatible `S` and `R`-module structures on `M` and a type `X`, the set of functions
+`X → M` is `S`-linearly equivalent to the `R`-linear maps from the free `R`-module
+on `X` to `M`. -/
+noncomputable def llift : (X → M) ≃ₗ[S] ((X →₀ R) →ₗ[R] M) :=
+{ map_smul' :=
+ begin
+ intros,
+ dsimp,
+ ext,
+ simp only [coe_comp, function.comp_app, lsingle_apply, lift_apply, pi.smul_apply,
+ sum_single_index, zero_smul, one_smul, linear_map.smul_apply],
+ end, ..lift M R X }
+
+@[simp] lemma llift_apply (f : X → M) (x : X →₀ R) :
+ llift M R S X f x = lift M R X f x := rfl
+
+@[simp] lemma llift_symm_apply (f : (X →₀ R) →ₗ[R] M) (x : X) :
+ (llift M R S X).symm f x = f (single x 1) := rfl
end
section lmap_domain
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(first ported)
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -244,7 +244,7 @@ theorem mem_supported {s : Set α} (p : α →₀ M) : p ∈ supported M R s ↔
#align finsupp.mem_supported Finsupp.mem_supported
-/
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x «expr ∉ » s) -/
#print Finsupp.mem_supported' /-
theorem mem_supported' {s : Set α} (p : α →₀ M) :
p ∈ supported M R s ↔ ∀ (x) (_ : x ∉ s), p x = 0 := by
@@ -598,7 +598,7 @@ theorem lmapDomain_supported [Nonempty α] (f : α → α') (s : Set α) :
#align finsupp.lmap_domain_supported Finsupp.lmapDomain_supported
-/
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (a b «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (a b «expr ∈ » s) -/
#print Finsupp.lmapDomain_disjoint_ker /-
theorem lmapDomain_disjoint_ker (f : α → α') {s : Set α}
(H : ∀ (a) (_ : a ∈ s) (b) (_ : b ∈ s), f a = f b → a = b) :
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -353,7 +353,7 @@ theorem supported_iUnion {δ : Type _} (s : δ → Set α) :
haveI := Classical.decPred fun x => x ∈ ⋃ i, s i
suffices
((Submodule.subtype _).comp (restrict_dom M R (⋃ i, s i))).range ≤ ⨆ i, supported M R (s i) by
- rwa [LinearMap.range_comp, range_restrict_dom, Submodule.map_top, range_subtype] at this
+ rwa [LinearMap.range_comp, range_restrict_dom, Submodule.map_top, range_subtype] at this
rw [range_le_iff_comap, eq_top_iff]
rintro l ⟨⟩
apply Finsupp.induction l; · exact zero_mem _
@@ -397,7 +397,7 @@ theorem disjoint_supported_supported_iff [Nontrivial M] {s t : Set α} :
refine' ⟨fun h => set.disjoint_left.mpr fun x hx1 hx2 => _, disjoint_supported_supported⟩
rcases exists_ne (0 : M) with ⟨y, hy⟩
have := h.le_bot ⟨single_mem_supported R y hx1, single_mem_supported R y hx2⟩
- rw [mem_bot, single_eq_zero] at this
+ rw [mem_bot, single_eq_zero] at this
exact hy this
#align finsupp.disjoint_supported_supported_iff Finsupp.disjoint_supported_supported_iff
-/
@@ -572,7 +572,7 @@ theorem supported_comap_lmapDomain (f : α → α') (s : Set α') :
fun l (hl : ↑l.support ⊆ f ⁻¹' s) =>
show ↑(mapDomain f l).support ⊆ s
by
- rw [← Set.image_subset_iff, ← Finset.coe_image] at hl
+ rw [← Set.image_subset_iff, ← Finset.coe_image] at hl
exact Set.Subset.trans map_domain_support hl
#align finsupp.supported_comap_lmap_domain Finsupp.supported_comap_lmapDomain
-/
@@ -606,12 +606,12 @@ theorem lmapDomain_disjoint_ker (f : α → α') {s : Set α}
by
rw [disjoint_iff_inf_le]
rintro l ⟨h₁, h₂⟩
- rw [SetLike.mem_coe, mem_ker, lmap_domain_apply, map_domain] at h₂
+ rw [SetLike.mem_coe, mem_ker, lmap_domain_apply, map_domain] at h₂
simp; ext x
haveI := Classical.decPred fun x => x ∈ s
by_cases xs : x ∈ s
· have : Finsupp.sum l (fun a => Finsupp.single (f a)) (f x) = 0 := by rw [h₂]; rfl
- rw [Finsupp.sum_apply, Finsupp.sum, Finset.sum_eq_single x] at this
+ rw [Finsupp.sum_apply, Finsupp.sum, Finset.sum_eq_single x] at this
· simpa [Finsupp.single_apply]
· intro y hy xy; simp [mt (H _ (h₁ hy) _ xs) xy]
· simp (config := { contextual := true })
@@ -738,7 +738,7 @@ theorem range_total : (Finsupp.total α M R v).range = span R (range v) :=
ext x
constructor
· intro hx
- rw [LinearMap.mem_range] at hx
+ rw [LinearMap.mem_range] at hx
rcases hx with ⟨l, hl⟩
rw [← hl]
rw [Finsupp.total_apply]
@@ -821,7 +821,7 @@ theorem span_image_eq_map_total (s : Set α) :
by
apply span_eq_of_le
· intro x hx
- rw [Set.mem_image] at hx
+ rw [Set.mem_image] at hx
apply Exists.elim hx
intro i hi
exact ⟨_, Finsupp.single_mem_supported R 1 hi.1, by simp [hi.2]⟩
@@ -1394,7 +1394,7 @@ theorem Submodule.exists_finset_of_mem_iSup {ι : Sort _} (p : ι → Submodule
have :=
CompleteLattice.IsCompactElement.exists_finset_of_le_iSup (Submodule R M)
(Submodule.singleton_span_isCompactElement m) p
- simp only [Submodule.span_singleton_le_iff_mem] at this
+ simp only [Submodule.span_singleton_le_iff_mem] at this
exact this hm
#align submodule.exists_finset_of_mem_supr Submodule.exists_finset_of_mem_iSup
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -204,6 +204,11 @@ theorem disjoint_lsingle_lsingle (s t : Set α) (hs : Disjoint s t) :
rw [disjoint_iff_inf_le]
refine' le_trans (le_iInf fun i => _) infi_ker_lapply_le_bot
classical
+ by_cases his : i ∈ s
+ · by_cases hit : i ∈ t
+ · exact (hs.le_bot ⟨his, hit⟩).elim
+ exact inf_le_of_right_le (iInf_le_of_le i <| iInf_le _ hit)
+ exact inf_le_of_left_le (iInf_le_of_le i <| iInf_le _ his)
#align finsupp.disjoint_lsingle_lsingle Finsupp.disjoint_lsingle_lsingle
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -204,11 +204,6 @@ theorem disjoint_lsingle_lsingle (s t : Set α) (hs : Disjoint s t) :
rw [disjoint_iff_inf_le]
refine' le_trans (le_iInf fun i => _) infi_ker_lapply_le_bot
classical
- by_cases his : i ∈ s
- · by_cases hit : i ∈ t
- · exact (hs.le_bot ⟨his, hit⟩).elim
- exact inf_le_of_right_le (iInf_le_of_le i <| iInf_le _ hit)
- exact inf_le_of_left_le (iInf_le_of_le i <| iInf_le _ his)
#align finsupp.disjoint_lsingle_lsingle Finsupp.disjoint_lsingle_lsingle
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,9 +3,9 @@ Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
-import Mathbin.Data.Finsupp.Defs
-import Mathbin.LinearAlgebra.Pi
-import Mathbin.LinearAlgebra.Span
+import Data.Finsupp.Defs
+import LinearAlgebra.Pi
+import LinearAlgebra.Span
#align_import linear_algebra.finsupp from "leanprover-community/mathlib"@"9d684a893c52e1d6692a504a118bfccbae04feeb"
@@ -244,7 +244,7 @@ theorem mem_supported {s : Set α} (p : α →₀ M) : p ∈ supported M R s ↔
#align finsupp.mem_supported Finsupp.mem_supported
-/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x «expr ∉ » s) -/
#print Finsupp.mem_supported' /-
theorem mem_supported' {s : Set α} (p : α →₀ M) :
p ∈ supported M R s ↔ ∀ (x) (_ : x ∉ s), p x = 0 := by
@@ -598,7 +598,7 @@ theorem lmapDomain_supported [Nonempty α] (f : α → α') (s : Set α) :
#align finsupp.lmap_domain_supported Finsupp.lmapDomain_supported
-/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a b «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (a b «expr ∈ » s) -/
#print Finsupp.lmapDomain_disjoint_ker /-
theorem lmapDomain_disjoint_ker (f : α → α') {s : Set α}
(H : ∀ (a) (_ : a ∈ s) (b) (_ : b ∈ s), f a = f b → a = b) :
mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504
@@ -1129,7 +1129,7 @@ def sumFinsuppLEquivProdFinsupp {α β : Type _} : (Sum α β →₀ M) ≃ₗ[R
{ sumFinsuppAddEquivProdFinsupp with
map_smul' := by intros;
ext <;>
- simp only [AddEquiv.toFun_eq_coe, Prod.smul_fst, Prod.smul_snd, smul_apply,
+ simp only [AddEquiv.to_fun_eq_coe, Prod.smul_fst, Prod.smul_snd, smul_apply,
snd_sum_finsupp_add_equiv_prod_finsupp, fst_sum_finsupp_add_equiv_prod_finsupp,
RingHom.id_apply] }
#align finsupp.sum_finsupp_lequiv_prod_finsupp Finsupp.sumFinsuppLEquivProdFinsupp
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,16 +2,13 @@
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-
-! This file was ported from Lean 3 source module linear_algebra.finsupp
-! leanprover-community/mathlib commit 9d684a893c52e1d6692a504a118bfccbae04feeb
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Data.Finsupp.Defs
import Mathbin.LinearAlgebra.Pi
import Mathbin.LinearAlgebra.Span
+#align_import linear_algebra.finsupp from "leanprover-community/mathlib"@"9d684a893c52e1d6692a504a118bfccbae04feeb"
+
/-!
# Properties of the module `α →₀ M`
@@ -247,7 +244,7 @@ theorem mem_supported {s : Set α} (p : α →₀ M) : p ∈ supported M R s ↔
#align finsupp.mem_supported Finsupp.mem_supported
-/
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ∉ » s) -/
#print Finsupp.mem_supported' /-
theorem mem_supported' {s : Set α} (p : α →₀ M) :
p ∈ supported M R s ↔ ∀ (x) (_ : x ∉ s), p x = 0 := by
@@ -601,7 +598,7 @@ theorem lmapDomain_supported [Nonempty α] (f : α → α') (s : Set α) :
#align finsupp.lmap_domain_supported Finsupp.lmapDomain_supported
-/
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (a b «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a b «expr ∈ » s) -/
#print Finsupp.lmapDomain_disjoint_ker /-
theorem lmapDomain_disjoint_ker (f : α → α') {s : Set α}
(H : ∀ (a) (_ : a ∈ s) (b) (_ : b ∈ s), f a = f b → a = b) :
mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303
@@ -315,7 +315,7 @@ end
theorem restrictDom_comp_subtype (s : Set α) :
(restrictDom M R s).comp (Submodule.subtype _) = LinearMap.id :=
by
- ext (l a)
+ ext l a
by_cases a ∈ s <;> simp [h]
exact ((mem_supported' R l.1).1 l.2 a h).symm
#align finsupp.restrict_dom_comp_subtype Finsupp.restrictDom_comp_subtype
@@ -438,10 +438,10 @@ def lsum : (α → M →ₗ[R] N) ≃ₗ[S] (α →₀ M) →ₗ[R] N
map_add' := (liftAddHom fun x => (F x).toAddMonoidHom).map_add
map_smul' := fun c f => by simp [sum_smul_index', smul_sum] }
invFun F x := F.comp (lsingle x)
- left_inv F := by ext (x y); simp
- right_inv F := by ext (x y); simp
- map_add' F G := by ext (x y); simp
- map_smul' F G := by ext (x y); simp
+ left_inv F := by ext x y; simp
+ right_inv F := by ext x y; simp
+ map_add' F G := by ext x y; simp
+ map_smul' F G := by ext x y; simp
#align finsupp.lsum Finsupp.lsum
-/
@@ -1469,7 +1469,7 @@ def splittingOfFinsuppSurjective (f : M →ₗ[R] α →₀ R) (s : Surjective f
theorem splittingOfFinsuppSurjective_splits (f : M →ₗ[R] α →₀ R) (s : Surjective f) :
f.comp (splittingOfFinsuppSurjective f s) = LinearMap.id :=
by
- ext (x y)
+ ext x y
dsimp [splitting_of_finsupp_surjective]
congr
rw [sum_single_index, one_smul]
@@ -1506,7 +1506,7 @@ def splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R) (s
theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : f.comp (splittingOfFunOnFintypeSurjective f s) = LinearMap.id :=
by
- ext (x y)
+ ext x y
dsimp [splitting_of_fun_on_fintype_surjective]
rw [linear_equiv_fun_on_finite_symm_single, Finsupp.sum_single_index, one_smul,
(s (Finsupp.single x 1)).choose_spec, Finsupp.single_eq_pi_single]
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -76,16 +76,21 @@ variable [AddCommMonoid N] [Module R N]
variable [AddCommMonoid P] [Module R P]
+#print Finsupp.lsingle /-
/-- Interpret `finsupp.single a` as a linear map. -/
def lsingle (a : α) : M →ₗ[R] α →₀ M :=
{ Finsupp.singleAddHom a with map_smul' := fun a b => (smul_single _ _ _).symm }
#align finsupp.lsingle Finsupp.lsingle
+-/
+#print Finsupp.lhom_ext /-
/-- Two `R`-linear maps from `finsupp X M` which agree on each `single x y` agree everywhere. -/
theorem lhom_ext ⦃φ ψ : (α →₀ M) →ₗ[R] N⦄ (h : ∀ a b, φ (single a b) = ψ (single a b)) : φ = ψ :=
LinearMap.toAddMonoidHom_injective <| addHom_ext h
#align finsupp.lhom_ext Finsupp.lhom_ext
+-/
+#print Finsupp.lhom_ext' /-
/-- Two `R`-linear maps from `finsupp X M` which agree on each `single x y` agree everywhere.
We formulate this fact using equality of linear maps `φ.comp (lsingle a)` and `ψ.comp (lsingle a)`
@@ -96,12 +101,16 @@ theorem lhom_ext' ⦃φ ψ : (α →₀ M) →ₗ[R] N⦄ (h : ∀ a, φ.comp (l
φ = ψ :=
lhom_ext fun a => LinearMap.congr_fun (h a)
#align finsupp.lhom_ext' Finsupp.lhom_ext'
+-/
+#print Finsupp.lapply /-
/-- Interpret `λ (f : α →₀ M), f a` as a linear map. -/
def lapply (a : α) : (α →₀ M) →ₗ[R] M :=
{ Finsupp.applyAddHom a with map_smul' := fun a b => rfl }
#align finsupp.lapply Finsupp.lapply
+-/
+#print Finsupp.lcoeFun /-
/-- Forget that a function is finitely supported.
This is the linear version of `finsupp.to_fun`. -/
@@ -111,11 +120,13 @@ def lcoeFun : (α →₀ M) →ₗ[R] α → M where
map_add' x y := by ext; simp
map_smul' x y := by ext; simp
#align finsupp.lcoe_fun Finsupp.lcoeFun
+-/
section LsubtypeDomain
variable (s : Set α)
+#print Finsupp.lsubtypeDomain /-
/-- Interpret `finsupp.subtype_domain s` as a linear map. -/
def lsubtypeDomain : (α →₀ M) →ₗ[R] s →₀ M
where
@@ -123,29 +134,39 @@ def lsubtypeDomain : (α →₀ M) →ₗ[R] s →₀ M
map_add' a b := subtypeDomain_add
map_smul' c a := ext fun a => rfl
#align finsupp.lsubtype_domain Finsupp.lsubtypeDomain
+-/
+#print Finsupp.lsubtypeDomain_apply /-
theorem lsubtypeDomain_apply (f : α →₀ M) :
(lsubtypeDomain s : (α →₀ M) →ₗ[R] s →₀ M) f = subtypeDomain (fun x => x ∈ s) f :=
rfl
#align finsupp.lsubtype_domain_apply Finsupp.lsubtypeDomain_apply
+-/
end LsubtypeDomain
+#print Finsupp.lsingle_apply /-
@[simp]
theorem lsingle_apply (a : α) (b : M) : (lsingle a : M →ₗ[R] α →₀ M) b = single a b :=
rfl
#align finsupp.lsingle_apply Finsupp.lsingle_apply
+-/
+#print Finsupp.lapply_apply /-
@[simp]
theorem lapply_apply (a : α) (f : α →₀ M) : (lapply a : (α →₀ M) →ₗ[R] M) f = f a :=
rfl
#align finsupp.lapply_apply Finsupp.lapply_apply
+-/
+#print Finsupp.ker_lsingle /-
@[simp]
theorem ker_lsingle (a : α) : (lsingle a : M →ₗ[R] α →₀ M).ker = ⊥ :=
ker_eq_bot_of_injective (single_injective a)
#align finsupp.ker_lsingle Finsupp.ker_lsingle
+-/
+#print Finsupp.lsingle_range_le_ker_lapply /-
theorem lsingle_range_le_ker_lapply (s t : Set α) (h : Disjoint s t) :
(⨆ a ∈ s, (lsingle a : M →ₗ[R] α →₀ M).range) ≤ ⨅ a ∈ t, ker (lapply a : (α →₀ M) →ₗ[R] M) :=
by
@@ -155,20 +176,26 @@ theorem lsingle_range_le_ker_lapply (s t : Set α) (h : Disjoint s t) :
have : a₁ ≠ a₂ := fun eq => h.le_bot ⟨h₁, Eq.symm ▸ h₂⟩
exact single_eq_of_ne this
#align finsupp.lsingle_range_le_ker_lapply Finsupp.lsingle_range_le_ker_lapply
+-/
+#print Finsupp.iInf_ker_lapply_le_bot /-
theorem iInf_ker_lapply_le_bot : (⨅ a, ker (lapply a : (α →₀ M) →ₗ[R] M)) ≤ ⊥ :=
by
simp only [SetLike.le_def, mem_infi, mem_ker, mem_bot, lapply_apply]
exact fun a h => Finsupp.ext h
#align finsupp.infi_ker_lapply_le_bot Finsupp.iInf_ker_lapply_le_bot
+-/
+#print Finsupp.iSup_lsingle_range /-
theorem iSup_lsingle_range : (⨆ a, (lsingle a : M →ₗ[R] α →₀ M).range) = ⊤ :=
by
refine' eq_top_iff.2 <| SetLike.le_def.2 fun f _ => _
rw [← sum_single f]
exact sum_mem fun a ha => Submodule.mem_iSup_of_mem a ⟨_, rfl⟩
#align finsupp.supr_lsingle_range Finsupp.iSup_lsingle_range
+-/
+#print Finsupp.disjoint_lsingle_lsingle /-
theorem disjoint_lsingle_lsingle (s t : Set α) (hs : Disjoint s t) :
Disjoint (⨆ a ∈ s, (lsingle a : M →ₗ[R] α →₀ M).range)
(⨆ a ∈ t, (lsingle a : M →ₗ[R] α →₀ M).range) :=
@@ -186,14 +213,18 @@ theorem disjoint_lsingle_lsingle (s t : Set α) (hs : Disjoint s t) :
exact inf_le_of_right_le (iInf_le_of_le i <| iInf_le _ hit)
exact inf_le_of_left_le (iInf_le_of_le i <| iInf_le _ his)
#align finsupp.disjoint_lsingle_lsingle Finsupp.disjoint_lsingle_lsingle
+-/
+#print Finsupp.span_single_image /-
theorem span_single_image (s : Set M) (a : α) :
Submodule.span R (single a '' s) = (Submodule.span R s).map (lsingle a : M →ₗ[R] α →₀ M) := by
rw [← span_image] <;> rfl
#align finsupp.span_single_image Finsupp.span_single_image
+-/
variable (M R)
+#print Finsupp.supported /-
/-- `finsupp.supported M R s` is the `R`-submodule of all `p : α →₀ M` such that `p.support ⊆ s`. -/
def supported (s : Set α) : Submodule R (α →₀ M) :=
by
@@ -206,29 +237,39 @@ def supported (s : Set α) : Submodule R (α →₀ M) :=
· intro a p hp
refine' subset.trans (Finset.coe_subset.2 support_smul) hp
#align finsupp.supported Finsupp.supported
+-/
variable {M}
+#print Finsupp.mem_supported /-
theorem mem_supported {s : Set α} (p : α →₀ M) : p ∈ supported M R s ↔ ↑p.support ⊆ s :=
Iff.rfl
#align finsupp.mem_supported Finsupp.mem_supported
+-/
/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x «expr ∉ » s) -/
+#print Finsupp.mem_supported' /-
theorem mem_supported' {s : Set α} (p : α →₀ M) :
p ∈ supported M R s ↔ ∀ (x) (_ : x ∉ s), p x = 0 := by
haveI := Classical.decPred fun x : α => x ∈ s <;>
simp [mem_supported, Set.subset_def, not_imp_comm]
#align finsupp.mem_supported' Finsupp.mem_supported'
+-/
+#print Finsupp.mem_supported_support /-
theorem mem_supported_support (p : α →₀ M) : p ∈ Finsupp.supported M R (p.support : Set α) := by
rw [Finsupp.mem_supported]
#align finsupp.mem_supported_support Finsupp.mem_supported_support
+-/
+#print Finsupp.single_mem_supported /-
theorem single_mem_supported {s : Set α} {a : α} (b : M) (h : a ∈ s) :
single a b ∈ supported M R s :=
Set.Subset.trans support_single_subset (Finset.singleton_subset_set_iff.2 h)
#align finsupp.single_mem_supported Finsupp.single_mem_supported
+-/
+#print Finsupp.supported_eq_span_single /-
theorem supported_eq_span_single (s : Set α) :
supported R R s = span R ((fun i => single i 1) '' s) :=
by
@@ -241,9 +282,11 @@ theorem supported_eq_span_single (s : Set α) :
apply subset_span
apply Set.mem_image_of_mem _ (hl il)
#align finsupp.supported_eq_span_single Finsupp.supported_eq_span_single
+-/
variable (M R)
+#print Finsupp.restrictDom /-
/-- Interpret `finsupp.filter s` as a linear map from `α →₀ M` to `supported M R s`. -/
def restrictDom (s : Set α) : (α →₀ M) →ₗ[R] supported M R s :=
LinearMap.codRestrict _
@@ -252,19 +295,23 @@ def restrictDom (s : Set α) : (α →₀ M) →ₗ[R] supported M R s :=
map_smul' := fun a l => filter_smul } fun l =>
(mem_supported' _ _).2 fun x => filter_apply_neg (· ∈ s) l
#align finsupp.restrict_dom Finsupp.restrictDom
+-/
variable {M R}
section
+#print Finsupp.restrictDom_apply /-
@[simp]
theorem restrictDom_apply (s : Set α) (l : α →₀ M) :
((restrictDom M R s : (α →₀ M) →ₗ[R] supported M R s) l : α →₀ M) = Finsupp.filter (· ∈ s) l :=
rfl
#align finsupp.restrict_dom_apply Finsupp.restrictDom_apply
+-/
end
+#print Finsupp.restrictDom_comp_subtype /-
theorem restrictDom_comp_subtype (s : Set α) :
(restrictDom M R s).comp (Submodule.subtype _) = LinearMap.id :=
by
@@ -272,26 +319,36 @@ theorem restrictDom_comp_subtype (s : Set α) :
by_cases a ∈ s <;> simp [h]
exact ((mem_supported' R l.1).1 l.2 a h).symm
#align finsupp.restrict_dom_comp_subtype Finsupp.restrictDom_comp_subtype
+-/
+#print Finsupp.range_restrictDom /-
theorem range_restrictDom (s : Set α) : (restrictDom M R s).range = ⊤ :=
range_eq_top.2 <|
Function.RightInverse.surjective <| LinearMap.congr_fun (restrictDom_comp_subtype s)
#align finsupp.range_restrict_dom Finsupp.range_restrictDom
+-/
+#print Finsupp.supported_mono /-
theorem supported_mono {s t : Set α} (st : s ⊆ t) : supported M R s ≤ supported M R t := fun l h =>
Set.Subset.trans h st
#align finsupp.supported_mono Finsupp.supported_mono
+-/
+#print Finsupp.supported_empty /-
@[simp]
theorem supported_empty : supported M R (∅ : Set α) = ⊥ :=
eq_bot_iff.2 fun l h => (Submodule.mem_bot R).2 <| by ext <;> simp_all [mem_supported']
#align finsupp.supported_empty Finsupp.supported_empty
+-/
+#print Finsupp.supported_univ /-
@[simp]
theorem supported_univ : supported M R (Set.univ : Set α) = ⊤ :=
eq_top_iff.2 fun l _ => Set.subset_univ _
#align finsupp.supported_univ Finsupp.supported_univ
+-/
+#print Finsupp.supported_iUnion /-
theorem supported_iUnion {δ : Type _} (s : δ → Set α) :
supported M R (⋃ i, s i) = ⨆ i, supported M R (s i) :=
by
@@ -308,25 +365,35 @@ theorem supported_iUnion {δ : Type _} (s : δ → Set α) :
· cases' h with i hi
exact le_iSup (fun i => supported M R (s i)) i (single_mem_supported R _ hi)
#align finsupp.supported_Union Finsupp.supported_iUnion
+-/
+#print Finsupp.supported_union /-
theorem supported_union (s t : Set α) : supported M R (s ∪ t) = supported M R s ⊔ supported M R t :=
by erw [Set.union_eq_iUnion, supported_Union, iSup_bool_eq] <;> rfl
#align finsupp.supported_union Finsupp.supported_union
+-/
+#print Finsupp.supported_iInter /-
theorem supported_iInter {ι : Type _} (s : ι → Set α) :
supported M R (⋂ i, s i) = ⨅ i, supported M R (s i) :=
Submodule.ext fun x => by simp [mem_supported, subset_Inter_iff]
#align finsupp.supported_Inter Finsupp.supported_iInter
+-/
+#print Finsupp.supported_inter /-
theorem supported_inter (s t : Set α) : supported M R (s ∩ t) = supported M R s ⊓ supported M R t :=
by rw [Set.inter_eq_iInter, supported_Inter, iInf_bool_eq] <;> rfl
#align finsupp.supported_inter Finsupp.supported_inter
+-/
+#print Finsupp.disjoint_supported_supported /-
theorem disjoint_supported_supported {s t : Set α} (h : Disjoint s t) :
Disjoint (supported M R s) (supported M R t) :=
disjoint_iff.2 <| by rw [← supported_inter, disjoint_iff_inter_eq_empty.1 h, supported_empty]
#align finsupp.disjoint_supported_supported Finsupp.disjoint_supported_supported
+-/
+#print Finsupp.disjoint_supported_supported_iff /-
theorem disjoint_supported_supported_iff [Nontrivial M] {s t : Set α} :
Disjoint (supported M R s) (supported M R t) ↔ Disjoint s t :=
by
@@ -336,7 +403,9 @@ theorem disjoint_supported_supported_iff [Nontrivial M] {s t : Set α} :
rw [mem_bot, single_eq_zero] at this
exact hy this
#align finsupp.disjoint_supported_supported_iff Finsupp.disjoint_supported_supported_iff
+-/
+#print Finsupp.supportedEquivFinsupp /-
/-- Interpret `finsupp.restrict_support_equiv` as a linear equivalence between
`supported M R s` and `s →₀ M`. -/
def supportedEquivFinsupp (s : Set α) : supported M R s ≃ₗ[R] s →₀ M :=
@@ -350,11 +419,13 @@ def supportedEquivFinsupp (s : Set α) : supported M R s ≃ₗ[R] s →₀ M :=
rw [this]
exact LinearMap.isLinear _
#align finsupp.supported_equiv_finsupp Finsupp.supportedEquivFinsupp
+-/
section Lsum
variable (S) [Module S N] [SMulCommClass R S N]
+#print Finsupp.lsum /-
/-- Lift a family of linear maps `M →ₗ[R] N` indexed by `x : α` to a linear map from `α →₀ M` to
`N` using `finsupp.sum`. This is an upgraded version of `finsupp.lift_add_hom`.
@@ -372,24 +443,33 @@ def lsum : (α → M →ₗ[R] N) ≃ₗ[S] (α →₀ M) →ₗ[R] N
map_add' F G := by ext (x y); simp
map_smul' F G := by ext (x y); simp
#align finsupp.lsum Finsupp.lsum
+-/
+#print Finsupp.coe_lsum /-
@[simp]
theorem coe_lsum (f : α → M →ₗ[R] N) : (lsum S f : (α →₀ M) → N) = fun d => d.Sum fun i => f i :=
rfl
#align finsupp.coe_lsum Finsupp.coe_lsum
+-/
+#print Finsupp.lsum_apply /-
theorem lsum_apply (f : α → M →ₗ[R] N) (l : α →₀ M) : Finsupp.lsum S f l = l.Sum fun b => f b :=
rfl
#align finsupp.lsum_apply Finsupp.lsum_apply
+-/
+#print Finsupp.lsum_single /-
theorem lsum_single (f : α → M →ₗ[R] N) (i : α) (m : M) :
Finsupp.lsum S f (Finsupp.single i m) = f i m :=
Finsupp.sum_single_index (f i).map_zero
#align finsupp.lsum_single Finsupp.lsum_single
+-/
+#print Finsupp.lsum_symm_apply /-
theorem lsum_symm_apply (f : (α →₀ M) →ₗ[R] N) (x : α) : (lsum S).symm f x = f.comp (lsingle x) :=
rfl
#align finsupp.lsum_symm_apply Finsupp.lsum_symm_apply
+-/
end Lsum
@@ -397,6 +477,7 @@ section
variable (M) (R) (X : Type _) (S) [Module S M] [SMulCommClass R S M]
+#print Finsupp.lift /-
/-- A slight rearrangement from `lsum` gives us
the bijection underlying the free-forgetful adjunction for R-modules.
-/
@@ -404,17 +485,23 @@ noncomputable def lift : (X → M) ≃+ ((X →₀ R) →ₗ[R] M) :=
(AddEquiv.arrowCongr (Equiv.refl X) (ringLmapEquivSelf R ℕ M).toAddEquiv.symm).trans
(lsum _ : _ ≃ₗ[ℕ] _).toAddEquiv
#align finsupp.lift Finsupp.lift
+-/
+#print Finsupp.lift_symm_apply /-
@[simp]
theorem lift_symm_apply (f) (x) : ((lift M R X).symm f) x = f (single x 1) :=
rfl
#align finsupp.lift_symm_apply Finsupp.lift_symm_apply
+-/
+#print Finsupp.lift_apply /-
@[simp]
theorem lift_apply (f) (g) : ((lift M R X) f) g = g.Sum fun x r => r • f x :=
rfl
#align finsupp.lift_apply Finsupp.lift_apply
+-/
+#print Finsupp.llift /-
/-- Given compatible `S` and `R`-module structures on `M` and a type `X`, the set of functions
`X → M` is `S`-linearly equivalent to the `R`-linear maps from the free `R`-module
on `X` to `M`. -/
@@ -427,17 +514,22 @@ noncomputable def llift : (X → M) ≃ₗ[S] (X →₀ R) →ₗ[R] M :=
simp only [coe_comp, Function.comp_apply, lsingle_apply, lift_apply, Pi.smul_apply,
sum_single_index, zero_smul, one_smul, LinearMap.smul_apply] }
#align finsupp.llift Finsupp.llift
+-/
+#print Finsupp.llift_apply /-
@[simp]
theorem llift_apply (f : X → M) (x : X →₀ R) : llift M R S X f x = lift M R X f x :=
rfl
#align finsupp.llift_apply Finsupp.llift_apply
+-/
+#print Finsupp.llift_symm_apply /-
@[simp]
theorem llift_symm_apply (f : (X →₀ R) →ₗ[R] M) (x : X) :
(llift M R S X).symm f x = f (single x 1) :=
rfl
#align finsupp.llift_symm_apply Finsupp.llift_symm_apply
+-/
end
@@ -445,6 +537,7 @@ section LmapDomain
variable {α' : Type _} {α'' : Type _} (M R)
+#print Finsupp.lmapDomain /-
/-- Interpret `finsupp.map_domain` as a linear map. -/
def lmapDomain (f : α → α') : (α →₀ M) →ₗ[R] α' →₀ M
where
@@ -452,23 +545,31 @@ def lmapDomain (f : α → α') : (α →₀ M) →ₗ[R] α' →₀ M
map_add' a b := mapDomain_add
map_smul' := mapDomain_smul
#align finsupp.lmap_domain Finsupp.lmapDomain
+-/
+#print Finsupp.lmapDomain_apply /-
@[simp]
theorem lmapDomain_apply (f : α → α') (l : α →₀ M) :
(lmapDomain M R f : (α →₀ M) →ₗ[R] α' →₀ M) l = mapDomain f l :=
rfl
#align finsupp.lmap_domain_apply Finsupp.lmapDomain_apply
+-/
+#print Finsupp.lmapDomain_id /-
@[simp]
theorem lmapDomain_id : (lmapDomain M R id : (α →₀ M) →ₗ[R] α →₀ M) = LinearMap.id :=
LinearMap.ext fun l => mapDomain_id
#align finsupp.lmap_domain_id Finsupp.lmapDomain_id
+-/
+#print Finsupp.lmapDomain_comp /-
theorem lmapDomain_comp (f : α → α') (g : α' → α'') :
lmapDomain M R (g ∘ f) = (lmapDomain M R g).comp (lmapDomain M R f) :=
LinearMap.ext fun l => mapDomain_comp
#align finsupp.lmap_domain_comp Finsupp.lmapDomain_comp
+-/
+#print Finsupp.supported_comap_lmapDomain /-
theorem supported_comap_lmapDomain (f : α → α') (s : Set α') :
supported M R (f ⁻¹' s) ≤ (supported M R s).comap (lmapDomain M R f) :=
fun l (hl : ↑l.support ⊆ f ⁻¹' s) =>
@@ -477,7 +578,9 @@ theorem supported_comap_lmapDomain (f : α → α') (s : Set α') :
rw [← Set.image_subset_iff, ← Finset.coe_image] at hl
exact Set.Subset.trans map_domain_support hl
#align finsupp.supported_comap_lmap_domain Finsupp.supported_comap_lmapDomain
+-/
+#print Finsupp.lmapDomain_supported /-
theorem lmapDomain_supported [Nonempty α] (f : α → α') (s : Set α) :
(supported M R s).map (lmapDomain M R f) = supported M R (f '' s) :=
by
@@ -496,8 +599,10 @@ theorem lmapDomain_supported [Nonempty α] (f : α → α') (s : Set α) :
refine' (map_domain_congr fun c hc => _).trans map_domain_id
exact Function.invFunOn_eq (by simpa using hl hc)
#align finsupp.lmap_domain_supported Finsupp.lmapDomain_supported
+-/
/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (a b «expr ∈ » s) -/
+#print Finsupp.lmapDomain_disjoint_ker /-
theorem lmapDomain_disjoint_ker (f : α → α') {s : Set α}
(H : ∀ (a) (_ : a ∈ s) (b) (_ : b ∈ s), f a = f b → a = b) :
Disjoint (supported M R s) (lmapDomain M R f).ker :=
@@ -515,6 +620,7 @@ theorem lmapDomain_disjoint_ker (f : α → α') {s : Set α}
· simp (config := { contextual := true })
· by_contra h; exact xs (h₁ <| Finsupp.mem_support_iff.2 h)
#align finsupp.lmap_domain_disjoint_ker Finsupp.lmapDomain_disjoint_ker
+-/
end LmapDomain
@@ -522,6 +628,7 @@ section LcomapDomain
variable {β : Type _} {R M}
+#print Finsupp.lcomapDomain /-
/-- Given `f : α → β` and a proof `hf` that `f` is injective, `lcomap_domain f hf` is the linear map
sending `l : β →₀ M` to the finitely supported function from `α` to `M` given by composing
`l` with `f`.
@@ -533,6 +640,7 @@ def lcomapDomain (f : α → β) (hf : Function.Injective f) : (β →₀ M) →
map_add' x y := by ext; simp
map_smul' c x := by ext; simp
#align finsupp.lcomap_domain Finsupp.lcomapDomain
+-/
end LcomapDomain
@@ -541,51 +649,68 @@ section Total
variable (α) {α' : Type _} (M) {M' : Type _} (R) [AddCommMonoid M'] [Module R M'] (v : α → M)
{v' : α' → M'}
+#print Finsupp.total /-
/-- Interprets (l : α →₀ R) as linear combination of the elements in the family (v : α → M) and
evaluates this linear combination. -/
protected def total : (α →₀ R) →ₗ[R] M :=
Finsupp.lsum ℕ fun i => LinearMap.id.smul_right (v i)
#align finsupp.total Finsupp.total
+-/
variable {α M v}
+#print Finsupp.total_apply /-
theorem total_apply (l : α →₀ R) : Finsupp.total α M R v l = l.Sum fun i a => a • v i :=
rfl
#align finsupp.total_apply Finsupp.total_apply
+-/
+#print Finsupp.total_apply_of_mem_supported /-
theorem total_apply_of_mem_supported {l : α →₀ R} {s : Finset α}
(hs : l ∈ supported R R (↑s : Set α)) : Finsupp.total α M R v l = s.Sum fun i => l i • v i :=
Finset.sum_subset hs fun x _ hxg =>
show l x • v x = 0 by rw [not_mem_support_iff.1 hxg, zero_smul]
#align finsupp.total_apply_of_mem_supported Finsupp.total_apply_of_mem_supported
+-/
+#print Finsupp.total_single /-
@[simp]
theorem total_single (c : R) (a : α) : Finsupp.total α M R v (single a c) = c • v a := by
simp [total_apply, sum_single_index]
#align finsupp.total_single Finsupp.total_single
+-/
+#print Finsupp.total_zero_apply /-
theorem total_zero_apply (x : α →₀ R) : (Finsupp.total α M R 0) x = 0 := by
simp [Finsupp.total_apply]
#align finsupp.total_zero_apply Finsupp.total_zero_apply
+-/
variable (α M)
+#print Finsupp.total_zero /-
@[simp]
theorem total_zero : Finsupp.total α M R 0 = 0 :=
LinearMap.ext (total_zero_apply R)
#align finsupp.total_zero Finsupp.total_zero
+-/
variable {α M}
+#print Finsupp.apply_total /-
theorem apply_total (f : M →ₗ[R] M') (v) (l : α →₀ R) :
f (Finsupp.total α M R v l) = Finsupp.total α M' R (f ∘ v) l := by
apply Finsupp.induction_linear l <;> simp (config := { contextual := true })
#align finsupp.apply_total Finsupp.apply_total
+-/
+#print Finsupp.total_unique /-
theorem total_unique [Unique α] (l : α →₀ R) (v) :
Finsupp.total α M R v l = l default • v default := by rw [← total_single, ← unique_single l]
#align finsupp.total_unique Finsupp.total_unique
+-/
+#print Finsupp.total_surjective /-
theorem total_surjective (h : Function.Surjective v) :
Function.Surjective (Finsupp.total α M R v) :=
by
@@ -593,18 +718,24 @@ theorem total_surjective (h : Function.Surjective v) :
obtain ⟨y, hy⟩ := h x
exact ⟨Finsupp.single y 1, by simp [hy]⟩
#align finsupp.total_surjective Finsupp.total_surjective
+-/
+#print Finsupp.total_range /-
theorem total_range (h : Function.Surjective v) : (Finsupp.total α M R v).range = ⊤ :=
range_eq_top.2 <| total_surjective R h
#align finsupp.total_range Finsupp.total_range
+-/
+#print Finsupp.total_id_surjective /-
/-- Any module is a quotient of a free module. This is stated as surjectivity of
`finsupp.total M M R id : (M →₀ R) →ₗ[R] M`. -/
theorem total_id_surjective (M) [AddCommMonoid M] [Module R M] :
Function.Surjective (Finsupp.total M M R id) :=
total_surjective R Function.surjective_id
#align finsupp.total_id_surjective Finsupp.total_id_surjective
+-/
+#print Finsupp.range_total /-
theorem range_total : (Finsupp.total α M R v).range = span R (range v) :=
by
ext x
@@ -622,54 +753,72 @@ theorem range_total : (Finsupp.total α M R v).range = span R (range v) :=
use Finsupp.single i 1
simp [hi]
#align finsupp.range_total Finsupp.range_total
+-/
+#print Finsupp.lmapDomain_total /-
theorem lmapDomain_total (f : α → α') (g : M →ₗ[R] M') (h : ∀ i, g (v i) = v' (f i)) :
(Finsupp.total α' M' R v').comp (lmapDomain R R f) = g.comp (Finsupp.total α M R v) := by
ext l <;> simp [total_apply, Finsupp.sum_mapDomain_index, add_smul, h]
#align finsupp.lmap_domain_total Finsupp.lmapDomain_total
+-/
+#print Finsupp.total_comp_lmapDomain /-
theorem total_comp_lmapDomain (f : α → α') :
(Finsupp.total α' M' R v').comp (Finsupp.lmapDomain R R f) = Finsupp.total α M' R (v' ∘ f) := by
ext; simp
#align finsupp.total_comp_lmap_domain Finsupp.total_comp_lmapDomain
+-/
+#print Finsupp.total_embDomain /-
@[simp]
theorem total_embDomain (f : α ↪ α') (l : α →₀ R) :
(Finsupp.total α' M' R v') (embDomain f l) = (Finsupp.total α M' R (v' ∘ f)) l := by
simp [total_apply, Finsupp.sum, support_emb_domain, emb_domain_apply]
#align finsupp.total_emb_domain Finsupp.total_embDomain
+-/
+#print Finsupp.total_mapDomain /-
@[simp]
theorem total_mapDomain (f : α → α') (l : α →₀ R) :
(Finsupp.total α' M' R v') (mapDomain f l) = (Finsupp.total α M' R (v' ∘ f)) l :=
LinearMap.congr_fun (total_comp_lmapDomain _ _) l
#align finsupp.total_map_domain Finsupp.total_mapDomain
+-/
+#print Finsupp.total_equivMapDomain /-
@[simp]
theorem total_equivMapDomain (f : α ≃ α') (l : α →₀ R) :
(Finsupp.total α' M' R v') (equivMapDomain f l) = (Finsupp.total α M' R (v' ∘ f)) l := by
rw [equiv_map_domain_eq_map_domain, total_map_domain]
#align finsupp.total_equiv_map_domain Finsupp.total_equivMapDomain
+-/
+#print Finsupp.span_eq_range_total /-
/-- A version of `finsupp.range_total` which is useful for going in the other direction -/
theorem span_eq_range_total (s : Set M) : span R s = (Finsupp.total s M R coe).range := by
rw [range_total, Subtype.range_coe_subtype, Set.setOf_mem_eq]
#align finsupp.span_eq_range_total Finsupp.span_eq_range_total
+-/
+#print Finsupp.mem_span_iff_total /-
theorem mem_span_iff_total (s : Set M) (x : M) :
x ∈ span R s ↔ ∃ l : s →₀ R, Finsupp.total s M R coe l = x :=
(SetLike.ext_iff.1 <| span_eq_range_total _ _) x
#align finsupp.mem_span_iff_total Finsupp.mem_span_iff_total
+-/
variable {R}
+#print Finsupp.mem_span_range_iff_exists_finsupp /-
theorem mem_span_range_iff_exists_finsupp {v : α → M} {x : M} :
x ∈ span R (range v) ↔ ∃ c : α →₀ R, (c.Sum fun i a => a • v i) = x := by
simp only [← Finsupp.range_total, LinearMap.mem_range, Finsupp.total_apply]
#align finsupp.mem_span_range_iff_exists_finsupp Finsupp.mem_span_range_iff_exists_finsupp
+-/
variable (R)
+#print Finsupp.span_image_eq_map_total /-
theorem span_image_eq_map_total (s : Set α) :
span R (v '' s) = Submodule.map (Finsupp.total α M R v) (supported R R s) :=
by
@@ -688,18 +837,24 @@ theorem span_image_eq_map_total (s : Set α) :
· simp [(Finsupp.mem_supported' R _).1 hz _ h]
refine' sum_mem _; simp [this]
#align finsupp.span_image_eq_map_total Finsupp.span_image_eq_map_total
+-/
+#print Finsupp.mem_span_image_iff_total /-
theorem mem_span_image_iff_total {s : Set α} {x : M} :
x ∈ span R (v '' s) ↔ ∃ l ∈ supported R R s, Finsupp.total α M R v l = x := by
rw [span_image_eq_map_total]; simp
#align finsupp.mem_span_image_iff_total Finsupp.mem_span_image_iff_total
+-/
+#print Finsupp.total_option /-
theorem total_option (v : Option α → M) (f : Option α →₀ R) :
Finsupp.total (Option α) M R v f =
f none • v none + Finsupp.total α M R (v ∘ Option.some) f.some :=
by rw [total_apply, sum_option_index_smul, total_apply]
#align finsupp.total_option Finsupp.total_option
+-/
+#print Finsupp.total_total /-
theorem total_total {α β : Type _} (A : α → M) (B : β → α →₀ R) (f : β →₀ R) :
Finsupp.total α M R A (Finsupp.total β (α →₀ R) R B f) =
Finsupp.total β M R (fun b => Finsupp.total α M R A (B b)) f :=
@@ -711,14 +866,18 @@ theorem total_total {α β : Type _} (A : α → M) (B : β → α →₀ R) (f
simp [sum_add_index, h₁, h₂, add_smul]
· simp [sum_single_index, sum_smul_index, smul_sum, mul_smul]
#align finsupp.total_total Finsupp.total_total
+-/
+#print Finsupp.total_fin_zero /-
@[simp]
theorem total_fin_zero (f : Fin 0 → M) : Finsupp.total (Fin 0) M R f = 0 := by ext i;
apply finZeroElim i
#align finsupp.total_fin_zero Finsupp.total_fin_zero
+-/
variable (α) (M) (v)
+#print Finsupp.totalOn /-
/-- `finsupp.total_on M v s` interprets `p : α →₀ R` as a linear combination of a
subset of the vectors in `v`, mapping it to the span of those vectors.
@@ -728,9 +887,11 @@ protected def totalOn (s : Set α) : supported R R s →ₗ[R] span R (v '' s) :
LinearMap.codRestrict _ ((Finsupp.total _ _ _ v).comp (Submodule.subtype (supported R R s)))
fun ⟨l, hl⟩ => (mem_span_image_iff_total _).2 ⟨l, hl, rfl⟩
#align finsupp.total_on Finsupp.totalOn
+-/
variable {α} {M} {v}
+#print Finsupp.totalOn_range /-
theorem totalOn_range (s : Set α) : (Finsupp.totalOn α M R v s).range = ⊤ :=
by
rw [Finsupp.totalOn, LinearMap.range_eq_map, LinearMap.map_codRestrict, ←
@@ -738,18 +899,24 @@ theorem totalOn_range (s : Set α) : (Finsupp.totalOn α M R v s).range = ⊤ :=
range_subtype]
exact (span_image_eq_map_total _ _).le
#align finsupp.total_on_range Finsupp.totalOn_range
+-/
+#print Finsupp.total_comp /-
theorem total_comp (f : α' → α) :
Finsupp.total α' M R (v ∘ f) = (Finsupp.total α M R v).comp (lmapDomain R R f) := by ext;
simp [total_apply]
#align finsupp.total_comp Finsupp.total_comp
+-/
+#print Finsupp.total_comapDomain /-
theorem total_comapDomain (f : α → α') (l : α' →₀ R) (hf : Set.InjOn f (f ⁻¹' ↑l.support)) :
Finsupp.total α M R v (Finsupp.comapDomain f l hf) =
(l.support.Preimage f hf).Sum fun i => l (f i) • v i :=
by rw [Finsupp.total_apply] <;> rfl
#align finsupp.total_comap_domain Finsupp.total_comapDomain
+-/
+#print Finsupp.total_onFinset /-
theorem total_onFinset {s : Finset α} {f : α → R} (g : α → M) (hf : ∀ a, f a ≠ 0 → a ∈ s) :
Finsupp.total α M R g (Finsupp.onFinset s f hf) = Finset.sum s fun x : α => f x • g x :=
by
@@ -759,9 +926,11 @@ theorem total_onFinset {s : Finset α} {f : α → R} (g : α → M) (hf : ∀ a
contrapose! h
simp [h]
#align finsupp.total_on_finset Finsupp.total_onFinset
+-/
end Total
+#print Finsupp.domLCongr /-
/-- An equivalence of domains induces a linear equivalence of finitely supported functions.
This is `finsupp.dom_congr` as a `linear_equiv`.
@@ -770,36 +939,48 @@ protected def domLCongr {α₁ α₂ : Type _} (e : α₁ ≃ α₂) : (α₁
(Finsupp.domCongr e : (α₁ →₀ M) ≃+ (α₂ →₀ M)).toLinearEquiv <| by
simpa only [equiv_map_domain_eq_map_domain, dom_congr_apply] using (lmap_domain M R e).map_smul
#align finsupp.dom_lcongr Finsupp.domLCongr
+-/
+#print Finsupp.domLCongr_apply /-
@[simp]
theorem domLCongr_apply {α₁ : Type _} {α₂ : Type _} (e : α₁ ≃ α₂) (v : α₁ →₀ M) :
(Finsupp.domLCongr e : _ ≃ₗ[R] _) v = Finsupp.domCongr e v :=
rfl
#align finsupp.dom_lcongr_apply Finsupp.domLCongr_apply
+-/
+#print Finsupp.domLCongr_refl /-
@[simp]
theorem domLCongr_refl : Finsupp.domLCongr (Equiv.refl α) = LinearEquiv.refl R (α →₀ M) :=
LinearEquiv.ext fun _ => equivMapDomain_refl _
#align finsupp.dom_lcongr_refl Finsupp.domLCongr_refl
+-/
+#print Finsupp.domLCongr_trans /-
theorem domLCongr_trans {α₁ α₂ α₃ : Type _} (f : α₁ ≃ α₂) (f₂ : α₂ ≃ α₃) :
(Finsupp.domLCongr f).trans (Finsupp.domLCongr f₂) =
(Finsupp.domLCongr (f.trans f₂) : (_ →₀ M) ≃ₗ[R] _) :=
LinearEquiv.ext fun _ => (equivMapDomain_trans _ _ _).symm
#align finsupp.dom_lcongr_trans Finsupp.domLCongr_trans
+-/
+#print Finsupp.domLCongr_symm /-
@[simp]
theorem domLCongr_symm {α₁ α₂ : Type _} (f : α₁ ≃ α₂) :
((Finsupp.domLCongr f).symm : (_ →₀ M) ≃ₗ[R] _) = Finsupp.domLCongr f.symm :=
LinearEquiv.ext fun x => rfl
#align finsupp.dom_lcongr_symm Finsupp.domLCongr_symm
+-/
+#print Finsupp.domLCongr_single /-
@[simp]
theorem domLCongr_single {α₁ : Type _} {α₂ : Type _} (e : α₁ ≃ α₂) (i : α₁) (m : M) :
(Finsupp.domLCongr e : _ ≃ₗ[R] _) (Finsupp.single i m) = Finsupp.single (e i) m := by
simp [Finsupp.domLCongr, Finsupp.domCongr, equiv_map_domain_single]
#align finsupp.dom_lcongr_single Finsupp.domLCongr_single
+-/
+#print Finsupp.congr /-
/-- An equivalence of sets induces a linear equivalence of `finsupp`s supported on those sets. -/
noncomputable def congr {α' : Type _} (s : Set α) (t : Set α') (e : s ≃ t) :
supported M R s ≃ₗ[R] supported M R t :=
@@ -809,7 +990,9 @@ noncomputable def congr {α' : Type _} (s : Set α) (t : Set α') (e : s ≃ t)
refine' Finsupp.supportedEquivFinsupp s ≪≫ₗ (_ ≪≫ₗ (Finsupp.supportedEquivFinsupp t).symm)
exact Finsupp.domLCongr e
#align finsupp.congr Finsupp.congr
+-/
+#print Finsupp.mapRange.linearMap /-
/-- `finsupp.map_range` as a `linear_map`. -/
@[simps]
def mapRange.linearMap (f : M →ₗ[R] N) : (α →₀ M) →ₗ[R] α →₀ N :=
@@ -819,26 +1002,34 @@ def mapRange.linearMap (f : M →ₗ[R] N) : (α →₀ M) →ₗ[R] α →₀ N
toFun := (mapRange f f.map_zero : (α →₀ M) → α →₀ N)
map_smul' := fun c v => mapRange_smul c v (f.map_smul c) }
#align finsupp.map_range.linear_map Finsupp.mapRange.linearMap
+-/
+#print Finsupp.mapRange.linearMap_id /-
@[simp]
theorem mapRange.linearMap_id :
mapRange.linearMap LinearMap.id = (LinearMap.id : (α →₀ M) →ₗ[R] _) :=
LinearMap.ext mapRange_id
#align finsupp.map_range.linear_map_id Finsupp.mapRange.linearMap_id
+-/
+#print Finsupp.mapRange.linearMap_comp /-
theorem mapRange.linearMap_comp (f : N →ₗ[R] P) (f₂ : M →ₗ[R] N) :
(mapRange.linearMap (f.comp f₂) : (α →₀ _) →ₗ[R] _) =
(mapRange.linearMap f).comp (mapRange.linearMap f₂) :=
LinearMap.ext <| mapRange_comp _ _ _ _ _
#align finsupp.map_range.linear_map_comp Finsupp.mapRange.linearMap_comp
+-/
+#print Finsupp.mapRange.linearMap_toAddMonoidHom /-
@[simp]
theorem mapRange.linearMap_toAddMonoidHom (f : M →ₗ[R] N) :
(mapRange.linearMap f).toAddMonoidHom =
(mapRange.addMonoidHom f.toAddMonoidHom : (α →₀ M) →+ _) :=
AddMonoidHom.ext fun _ => rfl
#align finsupp.map_range.linear_map_to_add_monoid_hom Finsupp.mapRange.linearMap_toAddMonoidHom
+-/
+#print Finsupp.mapRange.linearEquiv /-
/-- `finsupp.map_range` as a `linear_equiv`. -/
@[simps apply]
def mapRange.linearEquiv (e : M ≃ₗ[R] N) : (α →₀ M) ≃ₗ[R] α →₀ N :=
@@ -847,70 +1038,92 @@ def mapRange.linearEquiv (e : M ≃ₗ[R] N) : (α →₀ M) ≃ₗ[R] α →₀
toFun := mapRange e e.map_zero
invFun := mapRange e.symm e.symm.map_zero }
#align finsupp.map_range.linear_equiv Finsupp.mapRange.linearEquiv
+-/
+#print Finsupp.mapRange.linearEquiv_refl /-
@[simp]
theorem mapRange.linearEquiv_refl :
mapRange.linearEquiv (LinearEquiv.refl R M) = LinearEquiv.refl R (α →₀ M) :=
LinearEquiv.ext mapRange_id
#align finsupp.map_range.linear_equiv_refl Finsupp.mapRange.linearEquiv_refl
+-/
+#print Finsupp.mapRange.linearEquiv_trans /-
theorem mapRange.linearEquiv_trans (f : M ≃ₗ[R] N) (f₂ : N ≃ₗ[R] P) :
(mapRange.linearEquiv (f.trans f₂) : (α →₀ _) ≃ₗ[R] _) =
(mapRange.linearEquiv f).trans (mapRange.linearEquiv f₂) :=
LinearEquiv.ext <| mapRange_comp _ _ _ _ _
#align finsupp.map_range.linear_equiv_trans Finsupp.mapRange.linearEquiv_trans
+-/
+#print Finsupp.mapRange.linearEquiv_symm /-
@[simp]
theorem mapRange.linearEquiv_symm (f : M ≃ₗ[R] N) :
((mapRange.linearEquiv f).symm : (α →₀ _) ≃ₗ[R] _) = mapRange.linearEquiv f.symm :=
LinearEquiv.ext fun x => rfl
#align finsupp.map_range.linear_equiv_symm Finsupp.mapRange.linearEquiv_symm
+-/
+#print Finsupp.mapRange.linearEquiv_toAddEquiv /-
@[simp]
theorem mapRange.linearEquiv_toAddEquiv (f : M ≃ₗ[R] N) :
(mapRange.linearEquiv f).toAddEquiv = (mapRange.addEquiv f.toAddEquiv : (α →₀ M) ≃+ _) :=
AddEquiv.ext fun _ => rfl
#align finsupp.map_range.linear_equiv_to_add_equiv Finsupp.mapRange.linearEquiv_toAddEquiv
+-/
+#print Finsupp.mapRange.linearEquiv_toLinearMap /-
@[simp]
theorem mapRange.linearEquiv_toLinearMap (f : M ≃ₗ[R] N) :
(mapRange.linearEquiv f).toLinearMap = (mapRange.linearMap f.toLinearMap : (α →₀ M) →ₗ[R] _) :=
LinearMap.ext fun _ => rfl
#align finsupp.map_range.linear_equiv_to_linear_map Finsupp.mapRange.linearEquiv_toLinearMap
+-/
+#print Finsupp.lcongr /-
/-- An equivalence of domain and a linear equivalence of codomain induce a linear equivalence of the
corresponding finitely supported functions. -/
def lcongr {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N) : (ι →₀ M) ≃ₗ[R] κ →₀ N :=
(Finsupp.domLCongr e₁).trans (mapRange.linearEquiv e₂)
#align finsupp.lcongr Finsupp.lcongr
+-/
+#print Finsupp.lcongr_single /-
@[simp]
theorem lcongr_single {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N) (i : ι) (m : M) :
lcongr e₁ e₂ (Finsupp.single i m) = Finsupp.single (e₁ i) (e₂ m) := by simp [lcongr]
#align finsupp.lcongr_single Finsupp.lcongr_single
+-/
+#print Finsupp.lcongr_apply_apply /-
@[simp]
theorem lcongr_apply_apply {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N) (f : ι →₀ M) (k : κ) :
lcongr e₁ e₂ f k = e₂ (f (e₁.symm k)) :=
rfl
#align finsupp.lcongr_apply_apply Finsupp.lcongr_apply_apply
+-/
+#print Finsupp.lcongr_symm_single /-
theorem lcongr_symm_single {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N) (k : κ) (n : N) :
(lcongr e₁ e₂).symm (Finsupp.single k n) = Finsupp.single (e₁.symm k) (e₂.symm n) :=
by
apply_fun lcongr e₁ e₂ using (lcongr e₁ e₂).Injective
simp
#align finsupp.lcongr_symm_single Finsupp.lcongr_symm_single
+-/
+#print Finsupp.lcongr_symm /-
@[simp]
theorem lcongr_symm {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N) :
(lcongr e₁ e₂).symm = lcongr e₁.symm e₂.symm := by ext; rfl
#align finsupp.lcongr_symm Finsupp.lcongr_symm
+-/
section Sum
variable (R)
+#print Finsupp.sumFinsuppLEquivProdFinsupp /-
/-- The linear equivalence between `(α ⊕ β) →₀ M` and `(α →₀ M) × (β →₀ M)`.
This is the `linear_equiv` version of `finsupp.sum_finsupp_equiv_prod_finsupp`. -/
@@ -923,26 +1136,35 @@ def sumFinsuppLEquivProdFinsupp {α β : Type _} : (Sum α β →₀ M) ≃ₗ[R
snd_sum_finsupp_add_equiv_prod_finsupp, fst_sum_finsupp_add_equiv_prod_finsupp,
RingHom.id_apply] }
#align finsupp.sum_finsupp_lequiv_prod_finsupp Finsupp.sumFinsuppLEquivProdFinsupp
+-/
+#print Finsupp.fst_sumFinsuppLEquivProdFinsupp /-
theorem fst_sumFinsuppLEquivProdFinsupp {α β : Type _} (f : Sum α β →₀ M) (x : α) :
(sumFinsuppLEquivProdFinsupp R f).1 x = f (Sum.inl x) :=
rfl
#align finsupp.fst_sum_finsupp_lequiv_prod_finsupp Finsupp.fst_sumFinsuppLEquivProdFinsupp
+-/
+#print Finsupp.snd_sumFinsuppLEquivProdFinsupp /-
theorem snd_sumFinsuppLEquivProdFinsupp {α β : Type _} (f : Sum α β →₀ M) (y : β) :
(sumFinsuppLEquivProdFinsupp R f).2 y = f (Sum.inr y) :=
rfl
#align finsupp.snd_sum_finsupp_lequiv_prod_finsupp Finsupp.snd_sumFinsuppLEquivProdFinsupp
+-/
+#print Finsupp.sumFinsuppLEquivProdFinsupp_symm_inl /-
theorem sumFinsuppLEquivProdFinsupp_symm_inl {α β : Type _} (fg : (α →₀ M) × (β →₀ M)) (x : α) :
((sumFinsuppLEquivProdFinsupp R).symm fg) (Sum.inl x) = fg.1 x :=
rfl
#align finsupp.sum_finsupp_lequiv_prod_finsupp_symm_inl Finsupp.sumFinsuppLEquivProdFinsupp_symm_inl
+-/
+#print Finsupp.sumFinsuppLEquivProdFinsupp_symm_inr /-
theorem sumFinsuppLEquivProdFinsupp_symm_inr {α β : Type _} (fg : (α →₀ M) × (β →₀ M)) (y : β) :
((sumFinsuppLEquivProdFinsupp R).symm fg) (Sum.inr y) = fg.2 y :=
rfl
#align finsupp.sum_finsupp_lequiv_prod_finsupp_symm_inr Finsupp.sumFinsuppLEquivProdFinsupp_symm_inr
+-/
end Sum
@@ -952,6 +1174,7 @@ variable {η : Type _} [Fintype η] {ιs : η → Type _} [Zero α]
variable (R)
+#print Finsupp.sigmaFinsuppLEquivPiFinsupp /-
/-- On a `fintype η`, `finsupp.split` is a linear equivalence between
`(Σ (j : η), ιs j) →₀ M` and `Π j, (ιs j →₀ M)`.
@@ -960,24 +1183,30 @@ noncomputable def sigmaFinsuppLEquivPiFinsupp {M : Type _} {ιs : η → Type _}
[Module R M] : ((Σ j, ιs j) →₀ M) ≃ₗ[R] ∀ j, ιs j →₀ M :=
{ sigmaFinsuppAddEquivPiFinsupp with map_smul' := fun c f => by ext; simp }
#align finsupp.sigma_finsupp_lequiv_pi_finsupp Finsupp.sigmaFinsuppLEquivPiFinsupp
+-/
+#print Finsupp.sigmaFinsuppLEquivPiFinsupp_apply /-
@[simp]
theorem sigmaFinsuppLEquivPiFinsupp_apply {M : Type _} {ιs : η → Type _} [AddCommMonoid M]
[Module R M] (f : (Σ j, ιs j) →₀ M) (j i) : sigmaFinsuppLEquivPiFinsupp R f j i = f ⟨j, i⟩ :=
rfl
#align finsupp.sigma_finsupp_lequiv_pi_finsupp_apply Finsupp.sigmaFinsuppLEquivPiFinsupp_apply
+-/
+#print Finsupp.sigmaFinsuppLEquivPiFinsupp_symm_apply /-
@[simp]
theorem sigmaFinsuppLEquivPiFinsupp_symm_apply {M : Type _} {ιs : η → Type _} [AddCommMonoid M]
[Module R M] (f : ∀ j, ιs j →₀ M) (ji) :
(Finsupp.sigmaFinsuppLEquivPiFinsupp R).symm f ji = f ji.1 ji.2 :=
rfl
#align finsupp.sigma_finsupp_lequiv_pi_finsupp_symm_apply Finsupp.sigmaFinsuppLEquivPiFinsupp_symm_apply
+-/
end Sigma
section Prod
+#print Finsupp.finsuppProdLEquiv /-
/-- The linear equivalence between `α × β →₀ M` and `α →₀ β →₀ M`.
This is the `linear_equiv` version of `finsupp.finsupp_prod_equiv`. -/
@@ -988,19 +1217,24 @@ noncomputable def finsuppProdLEquiv {α β : Type _} (R : Type _) {M : Type _} [
map_add' := fun f g => by ext; simp [finsupp_prod_equiv, curry_apply]
map_smul' := fun c f => by ext; simp [finsupp_prod_equiv, curry_apply] }
#align finsupp.finsupp_prod_lequiv Finsupp.finsuppProdLEquiv
+-/
+#print Finsupp.finsuppProdLEquiv_apply /-
@[simp]
theorem finsuppProdLEquiv_apply {α β R M : Type _} [Semiring R] [AddCommMonoid M] [Module R M]
(f : α × β →₀ M) (x y) : finsuppProdLEquiv R f x y = f (x, y) := by
rw [finsupp_prod_lequiv, LinearEquiv.coe_mk, finsupp_prod_equiv, Finsupp.curry_apply]
#align finsupp.finsupp_prod_lequiv_apply Finsupp.finsuppProdLEquiv_apply
+-/
+#print Finsupp.finsuppProdLEquiv_symm_apply /-
@[simp]
theorem finsuppProdLEquiv_symm_apply {α β R M : Type _} [Semiring R] [AddCommMonoid M] [Module R M]
(f : α →₀ β →₀ M) (xy) : (finsuppProdLEquiv R).symm f xy = f xy.1 xy.2 := by
conv_rhs =>
rw [← (finsupp_prod_lequiv R).apply_symm_apply f, finsupp_prod_lequiv_apply, Prod.mk.eta]
#align finsupp.finsupp_prod_lequiv_symm_apply Finsupp.finsuppProdLEquiv_symm_apply
+-/
end Prod
@@ -1034,10 +1268,13 @@ protected def Fintype.total : (α → M) →ₗ[S] (α → R) →ₗ[R] M
variable {S}
+#print Fintype.total_apply /-
theorem Fintype.total_apply (f) : Fintype.total R S v f = ∑ i, f i • v i :=
rfl
#align fintype.total_apply Fintype.total_apply
+-/
+#print Fintype.total_apply_single /-
@[simp]
theorem Fintype.total_apply_single (i : α) (r : R) :
Fintype.total R S v (Pi.single i r) = r • v i :=
@@ -1045,9 +1282,11 @@ theorem Fintype.total_apply_single (i : α) (r : R) :
simp_rw [Fintype.total_apply, Pi.single_apply, ite_smul, zero_smul]
rw [Finset.sum_ite_eq', if_pos (Finset.mem_univ _)]
#align fintype.total_apply_single Fintype.total_apply_single
+-/
variable (S)
+#print Finsupp.total_eq_fintype_total_apply /-
theorem Finsupp.total_eq_fintype_total_apply (x : α → R) :
Finsupp.total α M R v ((Finsupp.linearEquivFunOnFinite R R α).symm x) = Fintype.total R S v x :=
by
@@ -1057,25 +1296,31 @@ theorem Finsupp.total_eq_fintype_total_apply (x : α → R) :
rw [finsupp.not_mem_support_iff.mp hx]
exact zero_smul _ _
#align finsupp.total_eq_fintype_total_apply Finsupp.total_eq_fintype_total_apply
+-/
+#print Finsupp.total_eq_fintype_total /-
theorem Finsupp.total_eq_fintype_total :
(Finsupp.total α M R v).comp (Finsupp.linearEquivFunOnFinite R R α).symm.toLinearMap =
Fintype.total R S v :=
LinearMap.ext <| Finsupp.total_eq_fintype_total_apply R S v
#align finsupp.total_eq_fintype_total Finsupp.total_eq_fintype_total
+-/
variable {S}
+#print Fintype.range_total /-
@[simp]
theorem Fintype.range_total : (Fintype.total R S v).range = Submodule.span R (Set.range v) := by
rw [← Finsupp.total_eq_fintype_total, LinearMap.range_comp, LinearEquiv.toLinearMap_eq_coe,
LinearEquiv.range, Submodule.map_top, Finsupp.range_total]
#align fintype.range_total Fintype.range_total
+-/
section SpanRange
variable {v} {x : M}
+#print mem_span_range_iff_exists_fun /-
/-- An element `x` lies in the span of `v` iff it can be written as sum `∑ cᵢ • vᵢ = x`.
-/
theorem mem_span_range_iff_exists_fun : x ∈ span R (range v) ↔ ∃ c : α → R, ∑ i, c i • v i = x :=
@@ -1084,7 +1329,9 @@ theorem mem_span_range_iff_exists_fun : x ∈ span R (range v) ↔ ∃ c : α
finsupp.equiv_fun_on_finite.surjective.exists, Finsupp.equivFunOnFinite_apply]
exact exists_congr fun c => Eq.congr_left <| Finsupp.sum_fintype _ _ fun i => zero_smul _ _
#align mem_span_range_iff_exists_fun mem_span_range_iff_exists_fun
+-/
+#print top_le_span_range_iff_forall_exists_fun /-
/-- A family `v : α → V` is generating `V` iff every element `(x : V)`
can be written as sum `∑ cᵢ • vᵢ = x`.
-/
@@ -1094,6 +1341,7 @@ theorem top_le_span_range_iff_forall_exists_fun :
simp_rw [← mem_span_range_iff_exists_fun]
exact ⟨fun h x => h trivial, fun h x _ => h x⟩
#align top_le_span_range_iff_forall_exists_fun top_le_span_range_iff_forall_exists_fun
+-/
end SpanRange
@@ -1107,13 +1355,16 @@ section
variable (R)
+#print Span.repr /-
/-- Pick some representation of `x : span R w` as a linear combination in `w`,
using the axiom of choice.
-/
irreducible_def Span.repr (w : Set M) (x : span R w) : w →₀ R :=
((Finsupp.mem_span_iff_total _ _ _).mp x.2).some
#align span.repr Span.repr
+-/
+#print Span.finsupp_total_repr /-
@[simp]
theorem Span.finsupp_total_repr {w : Set M} (x : span R w) :
Finsupp.total w M R coe (Span.repr R w x) = x :=
@@ -1121,19 +1372,25 @@ theorem Span.finsupp_total_repr {w : Set M} (x : span R w) :
rw [Span.repr]
exact ((Finsupp.mem_span_iff_total _ _ _).mp x.2).choose_spec
#align span.finsupp_total_repr Span.finsupp_total_repr
+-/
end
+#print Submodule.finsupp_sum_mem /-
protected theorem Submodule.finsupp_sum_mem {ι β : Type _} [Zero β] (S : Submodule R M) (f : ι →₀ β)
(g : ι → β → M) (h : ∀ c, f c ≠ 0 → g c (f c) ∈ S) : f.Sum g ∈ S :=
AddSubmonoidClass.finsupp_sum_mem S f g h
#align submodule.finsupp_sum_mem Submodule.finsupp_sum_mem
+-/
+#print LinearMap.map_finsupp_total /-
theorem LinearMap.map_finsupp_total (f : M →ₗ[R] N) {ι : Type _} {g : ι → M} (l : ι →₀ R) :
f (Finsupp.total ι M R g l) = Finsupp.total ι N R (f ∘ g) l := by
simp only [Finsupp.total_apply, Finsupp.total_apply, Finsupp.sum, f.map_sum, f.map_smul]
#align linear_map.map_finsupp_total LinearMap.map_finsupp_total
+-/
+#print Submodule.exists_finset_of_mem_iSup /-
theorem Submodule.exists_finset_of_mem_iSup {ι : Sort _} (p : ι → Submodule R M) {m : M}
(hm : m ∈ ⨆ i, p i) : ∃ s : Finset ι, m ∈ ⨆ i ∈ s, p i :=
by
@@ -1143,13 +1400,16 @@ theorem Submodule.exists_finset_of_mem_iSup {ι : Sort _} (p : ι → Submodule
simp only [Submodule.span_singleton_le_iff_mem] at this
exact this hm
#align submodule.exists_finset_of_mem_supr Submodule.exists_finset_of_mem_iSup
+-/
+#print Submodule.mem_iSup_iff_exists_finset /-
/-- `submodule.exists_finset_of_mem_supr` as an `iff` -/
theorem Submodule.mem_iSup_iff_exists_finset {ι : Sort _} {p : ι → Submodule R M} {m : M} :
(m ∈ ⨆ i, p i) ↔ ∃ s : Finset ι, m ∈ ⨆ i ∈ s, p i :=
⟨Submodule.exists_finset_of_mem_iSup p, fun ⟨_, hs⟩ =>
iSup_mono (fun i => (iSup_const_le : _ ≤ p i)) hs⟩
#align submodule.mem_supr_iff_exists_finset Submodule.mem_iSup_iff_exists_finset
+-/
#print mem_span_finset /-
theorem mem_span_finset {s : Finset M} {x : M} :
@@ -1163,6 +1423,7 @@ theorem mem_span_finset {s : Finset M} {x : M} :
#align mem_span_finset mem_span_finset
-/
+#print mem_span_set /-
/-- An element `m ∈ M` is contained in the `R`-submodule spanned by a set `s ⊆ M`, if and only if
`m` can be written as a finite `R`-linear combination of elements of `s`.
The implementation uses `finsupp.sum`. -/
@@ -1174,7 +1435,9 @@ theorem mem_span_set {m : M} {s : Set M} :
simp_rw [← exists_prop]
exact Finsupp.mem_span_image_iff_total R
#align mem_span_set mem_span_set
+-/
+#print Module.subsingletonEquiv /-
/-- If `subsingleton R`, then `M ≃ₗ[R] ι →₀ R` for any type `ι`. -/
@[simps]
def Module.subsingletonEquiv (R M ι : Type _) [Semiring R] [Subsingleton R] [AddCommMonoid M]
@@ -1186,6 +1449,7 @@ def Module.subsingletonEquiv (R M ι : Type _) [Semiring R] [Subsingleton R] [Ad
map_add' m n := (add_zero 0).symm
map_smul' r m := (smul_zero r).symm
#align module.subsingleton_equiv Module.subsingletonEquiv
+-/
namespace LinearMap
@@ -1193,12 +1457,15 @@ variable {R M} {α : Type _}
open Finsupp Function
+#print LinearMap.splittingOfFinsuppSurjective /-
-- See also `linear_map.splitting_of_fun_on_fintype_surjective`
/-- A surjective linear map to finitely supported functions has a splitting. -/
def splittingOfFinsuppSurjective (f : M →ₗ[R] α →₀ R) (s : Surjective f) : (α →₀ R) →ₗ[R] M :=
Finsupp.lift _ _ _ fun x : α => (s (Finsupp.single x 1)).some
#align linear_map.splitting_of_finsupp_surjective LinearMap.splittingOfFinsuppSurjective
+-/
+#print LinearMap.splittingOfFinsuppSurjective_splits /-
theorem splittingOfFinsuppSurjective_splits (f : M →ₗ[R] α →₀ R) (s : Surjective f) :
f.comp (splittingOfFinsuppSurjective f s) = LinearMap.id :=
by
@@ -1209,17 +1476,23 @@ theorem splittingOfFinsuppSurjective_splits (f : M →ₗ[R] α →₀ R) (s : S
· exact (s (Finsupp.single x 1)).choose_spec
· rw [zero_smul]
#align linear_map.splitting_of_finsupp_surjective_splits LinearMap.splittingOfFinsuppSurjective_splits
+-/
+#print LinearMap.leftInverse_splittingOfFinsuppSurjective /-
theorem leftInverse_splittingOfFinsuppSurjective (f : M →ₗ[R] α →₀ R) (s : Surjective f) :
LeftInverse f (splittingOfFinsuppSurjective f s) := fun g =>
LinearMap.congr_fun (splittingOfFinsuppSurjective_splits f s) g
#align linear_map.left_inverse_splitting_of_finsupp_surjective LinearMap.leftInverse_splittingOfFinsuppSurjective
+-/
+#print LinearMap.splittingOfFinsuppSurjective_injective /-
theorem splittingOfFinsuppSurjective_injective (f : M →ₗ[R] α →₀ R) (s : Surjective f) :
Injective (splittingOfFinsuppSurjective f s) :=
(leftInverse_splittingOfFinsuppSurjective f s).Injective
#align linear_map.splitting_of_finsupp_surjective_injective LinearMap.splittingOfFinsuppSurjective_injective
+-/
+#print LinearMap.splittingOfFunOnFintypeSurjective /-
-- See also `linear_map.splitting_of_finsupp_surjective`
/-- A surjective linear map to functions on a finite type has a splitting. -/
def splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R) (s : Surjective f) :
@@ -1227,7 +1500,9 @@ def splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R) (s
(Finsupp.lift _ _ _ fun x : α => (s (Finsupp.single x 1)).some).comp
(linearEquivFunOnFinite R R α).symm.toLinearMap
#align linear_map.splitting_of_fun_on_fintype_surjective LinearMap.splittingOfFunOnFintypeSurjective
+-/
+#print LinearMap.splittingOfFunOnFintypeSurjective_splits /-
theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : f.comp (splittingOfFunOnFintypeSurjective f s) = LinearMap.id :=
by
@@ -1237,16 +1512,21 @@ theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R]
(s (Finsupp.single x 1)).choose_spec, Finsupp.single_eq_pi_single]
rw [zero_smul]
#align linear_map.splitting_of_fun_on_fintype_surjective_splits LinearMap.splittingOfFunOnFintypeSurjective_splits
+-/
+#print LinearMap.leftInverse_splittingOfFunOnFintypeSurjective /-
theorem leftInverse_splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : LeftInverse f (splittingOfFunOnFintypeSurjective f s) := fun g =>
LinearMap.congr_fun (splittingOfFunOnFintypeSurjective_splits f s) g
#align linear_map.left_inverse_splitting_of_fun_on_fintype_surjective LinearMap.leftInverse_splittingOfFunOnFintypeSurjective
+-/
+#print LinearMap.splittingOfFunOnFintypeSurjective_injective /-
theorem splittingOfFunOnFintypeSurjective_injective [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : Injective (splittingOfFunOnFintypeSurjective f s) :=
(leftInverse_splittingOfFunOnFintypeSurjective f s).Injective
#align linear_map.splitting_of_fun_on_fintype_surjective_injective LinearMap.splittingOfFunOnFintypeSurjective_injective
+-/
end LinearMap
mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3
@@ -1078,7 +1078,7 @@ variable {v} {x : M}
/-- An element `x` lies in the span of `v` iff it can be written as sum `∑ cᵢ • vᵢ = x`.
-/
-theorem mem_span_range_iff_exists_fun : x ∈ span R (range v) ↔ ∃ c : α → R, (∑ i, c i • v i) = x :=
+theorem mem_span_range_iff_exists_fun : x ∈ span R (range v) ↔ ∃ c : α → R, ∑ i, c i • v i = x :=
by
simp only [Finsupp.mem_span_range_iff_exists_finsupp,
finsupp.equiv_fun_on_finite.surjective.exists, Finsupp.equivFunOnFinite_apply]
@@ -1089,7 +1089,7 @@ theorem mem_span_range_iff_exists_fun : x ∈ span R (range v) ↔ ∃ c : α
can be written as sum `∑ cᵢ • vᵢ = x`.
-/
theorem top_le_span_range_iff_forall_exists_fun :
- ⊤ ≤ span R (range v) ↔ ∀ x, ∃ c : α → R, (∑ i, c i • v i) = x :=
+ ⊤ ≤ span R (range v) ↔ ∀ x, ∃ c : α → R, ∑ i, c i • v i = x :=
by
simp_rw [← mem_span_range_iff_exists_fun]
exact ⟨fun h x => h trivial, fun h x _ => h x⟩
@@ -1153,7 +1153,7 @@ theorem Submodule.mem_iSup_iff_exists_finset {ι : Sort _} {p : ι → Submodule
#print mem_span_finset /-
theorem mem_span_finset {s : Finset M} {x : M} :
- x ∈ span R (↑s : Set M) ↔ ∃ f : M → R, (∑ i in s, f i • i) = x :=
+ x ∈ span R (↑s : Set M) ↔ ∃ f : M → R, ∑ i in s, f i • i = x :=
⟨fun hx =>
let ⟨v, hvs, hvx⟩ :=
(Finsupp.mem_span_image_iff_total _).1
mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004
@@ -213,7 +213,7 @@ theorem mem_supported {s : Set α} (p : α →₀ M) : p ∈ supported M R s ↔
Iff.rfl
#align finsupp.mem_supported Finsupp.mem_supported
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x «expr ∉ » s) -/
theorem mem_supported' {s : Set α} (p : α →₀ M) :
p ∈ supported M R s ↔ ∀ (x) (_ : x ∉ s), p x = 0 := by
haveI := Classical.decPred fun x : α => x ∈ s <;>
@@ -497,7 +497,7 @@ theorem lmapDomain_supported [Nonempty α] (f : α → α') (s : Set α) :
exact Function.invFunOn_eq (by simpa using hl hc)
#align finsupp.lmap_domain_supported Finsupp.lmapDomain_supported
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a b «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (a b «expr ∈ » s) -/
theorem lmapDomain_disjoint_ker (f : α → α') {s : Set α}
(H : ∀ (a) (_ : a ∈ s) (b) (_ : b ∈ s), f a = f b → a = b) :
Disjoint (supported M R s) (lmapDomain M R f).ker :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297
@@ -180,11 +180,11 @@ theorem disjoint_lsingle_lsingle (s t : Set α) (hs : Disjoint s t) :
rw [disjoint_iff_inf_le]
refine' le_trans (le_iInf fun i => _) infi_ker_lapply_le_bot
classical
- by_cases his : i ∈ s
- · by_cases hit : i ∈ t
- · exact (hs.le_bot ⟨his, hit⟩).elim
- exact inf_le_of_right_le (iInf_le_of_le i <| iInf_le _ hit)
- exact inf_le_of_left_le (iInf_le_of_le i <| iInf_le _ his)
+ by_cases his : i ∈ s
+ · by_cases hit : i ∈ t
+ · exact (hs.le_bot ⟨his, hit⟩).elim
+ exact inf_le_of_right_le (iInf_le_of_le i <| iInf_le _ hit)
+ exact inf_le_of_left_le (iInf_le_of_le i <| iInf_le _ his)
#align finsupp.disjoint_lsingle_lsingle Finsupp.disjoint_lsingle_lsingle
theorem span_single_image (s : Set M) (a : α) :
@@ -197,7 +197,7 @@ variable (M R)
/-- `finsupp.supported M R s` is the `R`-submodule of all `p : α →₀ M` such that `p.support ⊆ s`. -/
def supported (s : Set α) : Submodule R (α →₀ M) :=
by
- refine' ⟨{ p | ↑p.support ⊆ s }, _, _, _⟩
+ refine' ⟨{p | ↑p.support ⊆ s}, _, _, _⟩
· intro p q hp hq
refine' subset.trans (subset.trans (Finset.coe_subset.2 support_add) _) (union_subset hp hq)
rw [Finset.coe_union]
@@ -236,7 +236,7 @@ theorem supported_eq_span_single (s : Set α) :
· rintro _ ⟨_, hp, rfl⟩; exact single_mem_supported R 1 hp
· rw [← l.sum_single]
refine' sum_mem fun i il => _
- convert@smul_mem R (α →₀ R) _ _ _ _ (single i 1) (l i) _
+ convert @smul_mem R (α →₀ R) _ _ _ _ (single i 1) (l i) _
· simp
apply subset_span
apply Set.mem_image_of_mem _ (hl il)
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -299,7 +299,7 @@ theorem supported_iUnion {δ : Type _} (s : δ → Set α) :
haveI := Classical.decPred fun x => x ∈ ⋃ i, s i
suffices
((Submodule.subtype _).comp (restrict_dom M R (⋃ i, s i))).range ≤ ⨆ i, supported M R (s i) by
- rwa [LinearMap.range_comp, range_restrict_dom, Submodule.map_top, range_subtype] at this
+ rwa [LinearMap.range_comp, range_restrict_dom, Submodule.map_top, range_subtype] at this
rw [range_le_iff_comap, eq_top_iff]
rintro l ⟨⟩
apply Finsupp.induction l; · exact zero_mem _
@@ -333,7 +333,7 @@ theorem disjoint_supported_supported_iff [Nontrivial M] {s t : Set α} :
refine' ⟨fun h => set.disjoint_left.mpr fun x hx1 hx2 => _, disjoint_supported_supported⟩
rcases exists_ne (0 : M) with ⟨y, hy⟩
have := h.le_bot ⟨single_mem_supported R y hx1, single_mem_supported R y hx2⟩
- rw [mem_bot, single_eq_zero] at this
+ rw [mem_bot, single_eq_zero] at this
exact hy this
#align finsupp.disjoint_supported_supported_iff Finsupp.disjoint_supported_supported_iff
@@ -474,7 +474,7 @@ theorem supported_comap_lmapDomain (f : α → α') (s : Set α') :
fun l (hl : ↑l.support ⊆ f ⁻¹' s) =>
show ↑(mapDomain f l).support ⊆ s
by
- rw [← Set.image_subset_iff, ← Finset.coe_image] at hl
+ rw [← Set.image_subset_iff, ← Finset.coe_image] at hl
exact Set.Subset.trans map_domain_support hl
#align finsupp.supported_comap_lmap_domain Finsupp.supported_comap_lmapDomain
@@ -504,12 +504,12 @@ theorem lmapDomain_disjoint_ker (f : α → α') {s : Set α}
by
rw [disjoint_iff_inf_le]
rintro l ⟨h₁, h₂⟩
- rw [SetLike.mem_coe, mem_ker, lmap_domain_apply, map_domain] at h₂
+ rw [SetLike.mem_coe, mem_ker, lmap_domain_apply, map_domain] at h₂
simp; ext x
haveI := Classical.decPred fun x => x ∈ s
by_cases xs : x ∈ s
· have : Finsupp.sum l (fun a => Finsupp.single (f a)) (f x) = 0 := by rw [h₂]; rfl
- rw [Finsupp.sum_apply, Finsupp.sum, Finset.sum_eq_single x] at this
+ rw [Finsupp.sum_apply, Finsupp.sum, Finset.sum_eq_single x] at this
· simpa [Finsupp.single_apply]
· intro y hy xy; simp [mt (H _ (h₁ hy) _ xs) xy]
· simp (config := { contextual := true })
@@ -610,7 +610,7 @@ theorem range_total : (Finsupp.total α M R v).range = span R (range v) :=
ext x
constructor
· intro hx
- rw [LinearMap.mem_range] at hx
+ rw [LinearMap.mem_range] at hx
rcases hx with ⟨l, hl⟩
rw [← hl]
rw [Finsupp.total_apply]
@@ -675,7 +675,7 @@ theorem span_image_eq_map_total (s : Set α) :
by
apply span_eq_of_le
· intro x hx
- rw [Set.mem_image] at hx
+ rw [Set.mem_image] at hx
apply Exists.elim hx
intro i hi
exact ⟨_, Finsupp.single_mem_supported R 1 hi.1, by simp [hi.2]⟩
@@ -917,7 +917,7 @@ This is the `linear_equiv` version of `finsupp.sum_finsupp_equiv_prod_finsupp`.
@[simps apply symm_apply]
def sumFinsuppLEquivProdFinsupp {α β : Type _} : (Sum α β →₀ M) ≃ₗ[R] (α →₀ M) × (β →₀ M) :=
{ sumFinsuppAddEquivProdFinsupp with
- map_smul' := by intros ;
+ map_smul' := by intros;
ext <;>
simp only [AddEquiv.toFun_eq_coe, Prod.smul_fst, Prod.smul_snd, smul_apply,
snd_sum_finsupp_add_equiv_prod_finsupp, fst_sum_finsupp_add_equiv_prod_finsupp,
@@ -957,13 +957,13 @@ variable (R)
This is the `linear_equiv` version of `finsupp.sigma_finsupp_add_equiv_pi_finsupp`. -/
noncomputable def sigmaFinsuppLEquivPiFinsupp {M : Type _} {ιs : η → Type _} [AddCommMonoid M]
- [Module R M] : ((Σj, ιs j) →₀ M) ≃ₗ[R] ∀ j, ιs j →₀ M :=
+ [Module R M] : ((Σ j, ιs j) →₀ M) ≃ₗ[R] ∀ j, ιs j →₀ M :=
{ sigmaFinsuppAddEquivPiFinsupp with map_smul' := fun c f => by ext; simp }
#align finsupp.sigma_finsupp_lequiv_pi_finsupp Finsupp.sigmaFinsuppLEquivPiFinsupp
@[simp]
theorem sigmaFinsuppLEquivPiFinsupp_apply {M : Type _} {ιs : η → Type _} [AddCommMonoid M]
- [Module R M] (f : (Σj, ιs j) →₀ M) (j i) : sigmaFinsuppLEquivPiFinsupp R f j i = f ⟨j, i⟩ :=
+ [Module R M] (f : (Σ j, ιs j) →₀ M) (j i) : sigmaFinsuppLEquivPiFinsupp R f j i = f ⟨j, i⟩ :=
rfl
#align finsupp.sigma_finsupp_lequiv_pi_finsupp_apply Finsupp.sigmaFinsuppLEquivPiFinsupp_apply
@@ -1140,7 +1140,7 @@ theorem Submodule.exists_finset_of_mem_iSup {ι : Sort _} (p : ι → Submodule
have :=
CompleteLattice.IsCompactElement.exists_finset_of_le_iSup (Submodule R M)
(Submodule.singleton_span_isCompactElement m) p
- simp only [Submodule.span_singleton_le_iff_mem] at this
+ simp only [Submodule.span_singleton_le_iff_mem] at this
exact this hm
#align submodule.exists_finset_of_mem_supr Submodule.exists_finset_of_mem_iSup
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -919,7 +919,7 @@ def sumFinsuppLEquivProdFinsupp {α β : Type _} : (Sum α β →₀ M) ≃ₗ[R
{ sumFinsuppAddEquivProdFinsupp with
map_smul' := by intros ;
ext <;>
- simp only [[anonymous], Prod.smul_fst, Prod.smul_snd, smul_apply,
+ simp only [AddEquiv.toFun_eq_coe, Prod.smul_fst, Prod.smul_snd, smul_apply,
snd_sum_finsupp_add_equiv_prod_finsupp, fst_sum_finsupp_add_equiv_prod_finsupp,
RingHom.id_apply] }
#align finsupp.sum_finsupp_lequiv_prod_finsupp Finsupp.sumFinsuppLEquivProdFinsupp
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -64,7 +64,7 @@ noncomputable section
open Set LinearMap Submodule
-open Classical BigOperators
+open scoped Classical BigOperators
namespace Finsupp
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -76,28 +76,16 @@ variable [AddCommMonoid N] [Module R N]
variable [AddCommMonoid P] [Module R P]
-/- warning: finsupp.lsingle -> Finsupp.lsingle is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], α -> (LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))
-but is expected to have type
- forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], α -> (LinearMap.{u3, u3, u2, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))
-Case conversion may be inaccurate. Consider using '#align finsupp.lsingle Finsupp.lsingleₓ'. -/
/-- Interpret `finsupp.single a` as a linear map. -/
def lsingle (a : α) : M →ₗ[R] α →₀ M :=
{ Finsupp.singleAddHom a with map_smul' := fun a b => (smul_single _ _ _).symm }
#align finsupp.lsingle Finsupp.lsingle
-/- warning: finsupp.lhom_ext -> Finsupp.lhom_ext is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.lhom_ext Finsupp.lhom_extₓ'. -/
/-- Two `R`-linear maps from `finsupp X M` which agree on each `single x y` agree everywhere. -/
theorem lhom_ext ⦃φ ψ : (α →₀ M) →ₗ[R] N⦄ (h : ∀ a b, φ (single a b) = ψ (single a b)) : φ = ψ :=
LinearMap.toAddMonoidHom_injective <| addHom_ext h
#align finsupp.lhom_ext Finsupp.lhom_ext
-/- warning: finsupp.lhom_ext' -> Finsupp.lhom_ext' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.lhom_ext' Finsupp.lhom_ext'ₓ'. -/
/-- Two `R`-linear maps from `finsupp X M` which agree on each `single x y` agree everywhere.
We formulate this fact using equality of linear maps `φ.comp (lsingle a)` and `ψ.comp (lsingle a)`
@@ -109,23 +97,11 @@ theorem lhom_ext' ⦃φ ψ : (α →₀ M) →ₗ[R] N⦄ (h : ∀ a, φ.comp (l
lhom_ext fun a => LinearMap.congr_fun (h a)
#align finsupp.lhom_ext' Finsupp.lhom_ext'
-/- warning: finsupp.lapply -> Finsupp.lapply is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], α -> (LinearMap.{u3, u3, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4)
-but is expected to have type
- forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], α -> (LinearMap.{u3, u3, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4)
-Case conversion may be inaccurate. Consider using '#align finsupp.lapply Finsupp.lapplyₓ'. -/
/-- Interpret `λ (f : α →₀ M), f a` as a linear map. -/
def lapply (a : α) : (α →₀ M) →ₗ[R] M :=
{ Finsupp.applyAddHom a with map_smul' := fun a b => rfl }
#align finsupp.lapply Finsupp.lapply
-/- warning: finsupp.lcoe_fun -> Finsupp.lcoeFun is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], LinearMap.{u3, u3, max u1 u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (α -> M) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Pi.Function.module.{u1, u3, u2} α R M _inst_1 _inst_3 _inst_4)
-but is expected to have type
- forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], LinearMap.{u3, u3, max u2 u1, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (α -> M) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Pi.module.{u1, u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.499 : α) => M) R _inst_1 (fun (i : α) => _inst_3) (fun (i : α) => _inst_4))
-Case conversion may be inaccurate. Consider using '#align finsupp.lcoe_fun Finsupp.lcoeFunₓ'. -/
/-- Forget that a function is finitely supported.
This is the linear version of `finsupp.to_fun`. -/
@@ -140,12 +116,6 @@ section LsubtypeDomain
variable (s : Set α)
-/- warning: finsupp.lsubtype_domain -> Finsupp.lsubtypeDomain is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α), LinearMap.{u3, u3, max u1 u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) M R _inst_1 _inst_3 _inst_4)
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/-- Interpret `finsupp.subtype_domain s` as a linear map. -/
def lsubtypeDomain : (α →₀ M) →ₗ[R] s →₀ M
where
@@ -154,12 +124,6 @@ def lsubtypeDomain : (α →₀ M) →ₗ[R] s →₀ M
map_smul' c a := ext fun a => rfl
#align finsupp.lsubtype_domain Finsupp.lsubtypeDomain
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theorem lsubtypeDomain_apply (f : α →₀ M) :
(lsubtypeDomain s : (α →₀ M) →ₗ[R] s →₀ M) f = subtypeDomain (fun x => x ∈ s) f :=
rfl
@@ -167,42 +131,21 @@ theorem lsubtypeDomain_apply (f : α →₀ M) :
end LsubtypeDomain
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@[simp]
theorem lsingle_apply (a : α) (b : M) : (lsingle a : M →ₗ[R] α →₀ M) b = single a b :=
rfl
#align finsupp.lsingle_apply Finsupp.lsingle_apply
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@[simp]
theorem lapply_apply (a : α) (f : α →₀ M) : (lapply a : (α →₀ M) →ₗ[R] M) f = f a :=
rfl
#align finsupp.lapply_apply Finsupp.lapply_apply
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@[simp]
theorem ker_lsingle (a : α) : (lsingle a : M →ₗ[R] α →₀ M).ker = ⊥ :=
ker_eq_bot_of_injective (single_injective a)
#align finsupp.ker_lsingle Finsupp.ker_lsingle
-/- warning: finsupp.lsingle_range_le_ker_lapply -> Finsupp.lsingle_range_le_ker_lapply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.lsingle_range_le_ker_lapply Finsupp.lsingle_range_le_ker_lapplyₓ'. -/
theorem lsingle_range_le_ker_lapply (s t : Set α) (h : Disjoint s t) :
(⨆ a ∈ s, (lsingle a : M →ₗ[R] α →₀ M).range) ≤ ⨅ a ∈ t, ker (lapply a : (α →₀ M) →ₗ[R] M) :=
by
@@ -213,24 +156,12 @@ theorem lsingle_range_le_ker_lapply (s t : Set α) (h : Disjoint s t) :
exact single_eq_of_ne this
#align finsupp.lsingle_range_le_ker_lapply Finsupp.lsingle_range_le_ker_lapply
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-Case conversion may be inaccurate. Consider using '#align finsupp.infi_ker_lapply_le_bot Finsupp.iInf_ker_lapply_le_botₓ'. -/
theorem iInf_ker_lapply_le_bot : (⨅ a, ker (lapply a : (α →₀ M) →ₗ[R] M)) ≤ ⊥ :=
by
simp only [SetLike.le_def, mem_infi, mem_ker, mem_bot, lapply_apply]
exact fun a h => Finsupp.ext h
#align finsupp.infi_ker_lapply_le_bot Finsupp.iInf_ker_lapply_le_bot
-/- warning: finsupp.supr_lsingle_range -> Finsupp.iSup_lsingle_range is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align finsupp.supr_lsingle_range Finsupp.iSup_lsingle_rangeₓ'. -/
theorem iSup_lsingle_range : (⨆ a, (lsingle a : M →ₗ[R] α →₀ M).range) = ⊤ :=
by
refine' eq_top_iff.2 <| SetLike.le_def.2 fun f _ => _
@@ -238,9 +169,6 @@ theorem iSup_lsingle_range : (⨆ a, (lsingle a : M →ₗ[R] α →₀ M).range
exact sum_mem fun a ha => Submodule.mem_iSup_of_mem a ⟨_, rfl⟩
#align finsupp.supr_lsingle_range Finsupp.iSup_lsingle_range
-/- warning: finsupp.disjoint_lsingle_lsingle -> Finsupp.disjoint_lsingle_lsingle is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.disjoint_lsingle_lsingle Finsupp.disjoint_lsingle_lsingleₓ'. -/
theorem disjoint_lsingle_lsingle (s t : Set α) (hs : Disjoint s t) :
Disjoint (⨆ a ∈ s, (lsingle a : M →ₗ[R] α →₀ M).range)
(⨆ a ∈ t, (lsingle a : M →ₗ[R] α →₀ M).range) :=
@@ -259,12 +187,6 @@ theorem disjoint_lsingle_lsingle (s t : Set α) (hs : Disjoint s t) :
exact inf_le_of_left_le (iInf_le_of_le i <| iInf_le _ his)
#align finsupp.disjoint_lsingle_lsingle Finsupp.disjoint_lsingle_lsingle
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-Case conversion may be inaccurate. Consider using '#align finsupp.span_single_image Finsupp.span_single_imageₓ'. -/
theorem span_single_image (s : Set M) (a : α) :
Submodule.span R (single a '' s) = (Submodule.span R s).map (lsingle a : M →ₗ[R] α →₀ M) := by
rw [← span_image] <;> rfl
@@ -272,12 +194,6 @@ theorem span_single_image (s : Set M) (a : α) :
variable (M R)
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-Case conversion may be inaccurate. Consider using '#align finsupp.supported Finsupp.supportedₓ'. -/
/-- `finsupp.supported M R s` is the `R`-submodule of all `p : α →₀ M` such that `p.support ⊆ s`. -/
def supported (s : Set α) : Submodule R (α →₀ M) :=
by
@@ -293,22 +209,10 @@ def supported (s : Set α) : Submodule R (α →₀ M) :=
variable {M}
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theorem mem_supported {s : Set α} (p : α →₀ M) : p ∈ supported M R s ↔ ↑p.support ⊆ s :=
Iff.rfl
#align finsupp.mem_supported Finsupp.mem_supported
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/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ∉ » s) -/
theorem mem_supported' {s : Set α} (p : α →₀ M) :
p ∈ supported M R s ↔ ∀ (x) (_ : x ∉ s), p x = 0 := by
@@ -316,33 +220,15 @@ theorem mem_supported' {s : Set α} (p : α →₀ M) :
simp [mem_supported, Set.subset_def, not_imp_comm]
#align finsupp.mem_supported' Finsupp.mem_supported'
-/- warning: finsupp.mem_supported_support -> Finsupp.mem_supported_support is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align finsupp.mem_supported_support Finsupp.mem_supported_supportₓ'. -/
theorem mem_supported_support (p : α →₀ M) : p ∈ Finsupp.supported M R (p.support : Set α) := by
rw [Finsupp.mem_supported]
#align finsupp.mem_supported_support Finsupp.mem_supported_support
-/- warning: finsupp.single_mem_supported -> Finsupp.single_mem_supported is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align finsupp.single_mem_supported Finsupp.single_mem_supportedₓ'. -/
theorem single_mem_supported {s : Set α} {a : α} (b : M) (h : a ∈ s) :
single a b ∈ supported M R s :=
Set.Subset.trans support_single_subset (Finset.singleton_subset_set_iff.2 h)
#align finsupp.single_mem_supported Finsupp.single_mem_supported
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-Case conversion may be inaccurate. Consider using '#align finsupp.supported_eq_span_single Finsupp.supported_eq_span_singleₓ'. -/
theorem supported_eq_span_single (s : Set α) :
supported R R s = span R ((fun i => single i 1) '' s) :=
by
@@ -358,12 +244,6 @@ theorem supported_eq_span_single (s : Set α) :
variable (M R)
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-Case conversion may be inaccurate. Consider using '#align finsupp.restrict_dom Finsupp.restrictDomₓ'. -/
/-- Interpret `finsupp.filter s` as a linear map from `α →₀ M` to `supported M R s`. -/
def restrictDom (s : Set α) : (α →₀ M) →ₗ[R] supported M R s :=
LinearMap.codRestrict _
@@ -377,9 +257,6 @@ variable {M R}
section
-/- warning: finsupp.restrict_dom_apply -> Finsupp.restrictDom_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.restrict_dom_apply Finsupp.restrictDom_applyₓ'. -/
@[simp]
theorem restrictDom_apply (s : Set α) (l : α →₀ M) :
((restrictDom M R s : (α →₀ M) →ₗ[R] supported M R s) l : α →₀ M) = Finsupp.filter (· ∈ s) l :=
@@ -388,9 +265,6 @@ theorem restrictDom_apply (s : Set α) (l : α →₀ M) :
end
-/- warning: finsupp.restrict_dom_comp_subtype -> Finsupp.restrictDom_comp_subtype is a dubious translation:
-<too large>
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theorem restrictDom_comp_subtype (s : Set α) :
(restrictDom M R s).comp (Submodule.subtype _) = LinearMap.id :=
by
@@ -399,52 +273,25 @@ theorem restrictDom_comp_subtype (s : Set α) :
exact ((mem_supported' R l.1).1 l.2 a h).symm
#align finsupp.restrict_dom_comp_subtype Finsupp.restrictDom_comp_subtype
-/- warning: finsupp.range_restrict_dom -> Finsupp.range_restrictDom is a dubious translation:
-<too large>
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theorem range_restrictDom (s : Set α) : (restrictDom M R s).range = ⊤ :=
range_eq_top.2 <|
Function.RightInverse.surjective <| LinearMap.congr_fun (restrictDom_comp_subtype s)
#align finsupp.range_restrict_dom Finsupp.range_restrictDom
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theorem supported_mono {s t : Set α} (st : s ⊆ t) : supported M R s ≤ supported M R t := fun l h =>
Set.Subset.trans h st
#align finsupp.supported_mono Finsupp.supported_mono
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@[simp]
theorem supported_empty : supported M R (∅ : Set α) = ⊥ :=
eq_bot_iff.2 fun l h => (Submodule.mem_bot R).2 <| by ext <;> simp_all [mem_supported']
#align finsupp.supported_empty Finsupp.supported_empty
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@[simp]
theorem supported_univ : supported M R (Set.univ : Set α) = ⊤ :=
eq_top_iff.2 fun l _ => Set.subset_univ _
#align finsupp.supported_univ Finsupp.supported_univ
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theorem supported_iUnion {δ : Type _} (s : δ → Set α) :
supported M R (⋃ i, s i) = ⨆ i, supported M R (s i) :=
by
@@ -462,54 +309,24 @@ theorem supported_iUnion {δ : Type _} (s : δ → Set α) :
exact le_iSup (fun i => supported M R (s i)) i (single_mem_supported R _ hi)
#align finsupp.supported_Union Finsupp.supported_iUnion
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theorem supported_union (s t : Set α) : supported M R (s ∪ t) = supported M R s ⊔ supported M R t :=
by erw [Set.union_eq_iUnion, supported_Union, iSup_bool_eq] <;> rfl
#align finsupp.supported_union Finsupp.supported_union
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theorem supported_iInter {ι : Type _} (s : ι → Set α) :
supported M R (⋂ i, s i) = ⨅ i, supported M R (s i) :=
Submodule.ext fun x => by simp [mem_supported, subset_Inter_iff]
#align finsupp.supported_Inter Finsupp.supported_iInter
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theorem supported_inter (s t : Set α) : supported M R (s ∩ t) = supported M R s ⊓ supported M R t :=
by rw [Set.inter_eq_iInter, supported_Inter, iInf_bool_eq] <;> rfl
#align finsupp.supported_inter Finsupp.supported_inter
-/- warning: finsupp.disjoint_supported_supported -> Finsupp.disjoint_supported_supported is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align finsupp.disjoint_supported_supported Finsupp.disjoint_supported_supportedₓ'. -/
theorem disjoint_supported_supported {s t : Set α} (h : Disjoint s t) :
Disjoint (supported M R s) (supported M R t) :=
disjoint_iff.2 <| by rw [← supported_inter, disjoint_iff_inter_eq_empty.1 h, supported_empty]
#align finsupp.disjoint_supported_supported Finsupp.disjoint_supported_supported
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-Case conversion may be inaccurate. Consider using '#align finsupp.disjoint_supported_supported_iff Finsupp.disjoint_supported_supported_iffₓ'. -/
theorem disjoint_supported_supported_iff [Nontrivial M] {s t : Set α} :
Disjoint (supported M R s) (supported M R t) ↔ Disjoint s t :=
by
@@ -520,12 +337,6 @@ theorem disjoint_supported_supported_iff [Nontrivial M] {s t : Set α} :
exact hy this
#align finsupp.disjoint_supported_supported_iff Finsupp.disjoint_supported_supported_iff
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-Case conversion may be inaccurate. Consider using '#align finsupp.supported_equiv_finsupp Finsupp.supportedEquivFinsuppₓ'. -/
/-- Interpret `finsupp.restrict_support_equiv` as a linear equivalence between
`supported M R s` and `s →₀ M`. -/
def supportedEquivFinsupp (s : Set α) : supported M R s ≃ₗ[R] s →₀ M :=
@@ -544,9 +355,6 @@ section Lsum
variable (S) [Module S N] [SMulCommClass R S N]
-/- warning: finsupp.lsum -> Finsupp.lsum is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.lsum Finsupp.lsumₓ'. -/
/-- Lift a family of linear maps `M →ₗ[R] N` indexed by `x : α` to a linear map from `α →₀ M` to
`N` using `finsupp.sum`. This is an upgraded version of `finsupp.lift_add_hom`.
@@ -565,32 +373,20 @@ def lsum : (α → M →ₗ[R] N) ≃ₗ[S] (α →₀ M) →ₗ[R] N
map_smul' F G := by ext (x y); simp
#align finsupp.lsum Finsupp.lsum
-/- warning: finsupp.coe_lsum -> Finsupp.coe_lsum is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.coe_lsum Finsupp.coe_lsumₓ'. -/
@[simp]
theorem coe_lsum (f : α → M →ₗ[R] N) : (lsum S f : (α →₀ M) → N) = fun d => d.Sum fun i => f i :=
rfl
#align finsupp.coe_lsum Finsupp.coe_lsum
-/- warning: finsupp.lsum_apply -> Finsupp.lsum_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.lsum_apply Finsupp.lsum_applyₓ'. -/
theorem lsum_apply (f : α → M →ₗ[R] N) (l : α →₀ M) : Finsupp.lsum S f l = l.Sum fun b => f b :=
rfl
#align finsupp.lsum_apply Finsupp.lsum_apply
-/- warning: finsupp.lsum_single -> Finsupp.lsum_single is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.lsum_single Finsupp.lsum_singleₓ'. -/
theorem lsum_single (f : α → M →ₗ[R] N) (i : α) (m : M) :
Finsupp.lsum S f (Finsupp.single i m) = f i m :=
Finsupp.sum_single_index (f i).map_zero
#align finsupp.lsum_single Finsupp.lsum_single
-/- warning: finsupp.lsum_symm_apply -> Finsupp.lsum_symm_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.lsum_symm_apply Finsupp.lsum_symm_applyₓ'. -/
theorem lsum_symm_apply (f : (α →₀ M) →ₗ[R] N) (x : α) : (lsum S).symm f x = f.comp (lsingle x) :=
rfl
#align finsupp.lsum_symm_apply Finsupp.lsum_symm_apply
@@ -601,12 +397,6 @@ section
variable (M) (R) (X : Type _) (S) [Module S M] [SMulCommClass R S M]
-/- warning: finsupp.lift -> Finsupp.lift is a dubious translation:
-lean 3 declaration is
- forall (M : Type.{u1}) (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u3}), AddEquiv.{max u3 u1, max (max u3 u2) u1} (X -> M) (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (ᾰ : X) => M) (fun (i : X) => AddZeroClass.toHasAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.hasAdd.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align finsupp.lift Finsupp.liftₓ'. -/
/-- A slight rearrangement from `lsum` gives us
the bijection underlying the free-forgetful adjunction for R-modules.
-/
@@ -615,28 +405,16 @@ noncomputable def lift : (X → M) ≃+ ((X →₀ R) →ₗ[R] M) :=
(lsum _ : _ ≃ₗ[ℕ] _).toAddEquiv
#align finsupp.lift Finsupp.lift
-/- warning: finsupp.lift_symm_apply -> Finsupp.lift_symm_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.lift_symm_apply Finsupp.lift_symm_applyₓ'. -/
@[simp]
theorem lift_symm_apply (f) (x) : ((lift M R X).symm f) x = f (single x 1) :=
rfl
#align finsupp.lift_symm_apply Finsupp.lift_symm_apply
-/- warning: finsupp.lift_apply -> Finsupp.lift_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.lift_apply Finsupp.lift_applyₓ'. -/
@[simp]
theorem lift_apply (f) (g) : ((lift M R X) f) g = g.Sum fun x r => r • f x :=
rfl
#align finsupp.lift_apply Finsupp.lift_apply
-/- warning: finsupp.llift -> Finsupp.llift is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align finsupp.llift Finsupp.lliftₓ'. -/
/-- Given compatible `S` and `R`-module structures on `M` and a type `X`, the set of functions
`X → M` is `S`-linearly equivalent to the `R`-linear maps from the free `R`-module
on `X` to `M`. -/
@@ -650,17 +428,11 @@ noncomputable def llift : (X → M) ≃ₗ[S] (X →₀ R) →ₗ[R] M :=
sum_single_index, zero_smul, one_smul, LinearMap.smul_apply] }
#align finsupp.llift Finsupp.llift
-/- warning: finsupp.llift_apply -> Finsupp.llift_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.llift_apply Finsupp.llift_applyₓ'. -/
@[simp]
theorem llift_apply (f : X → M) (x : X →₀ R) : llift M R S X f x = lift M R X f x :=
rfl
#align finsupp.llift_apply Finsupp.llift_apply
-/- warning: finsupp.llift_symm_apply -> Finsupp.llift_symm_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.llift_symm_apply Finsupp.llift_symm_applyₓ'. -/
@[simp]
theorem llift_symm_apply (f : (X →₀ R) →ₗ[R] M) (x : X) :
(llift M R S X).symm f x = f (single x 1) :=
@@ -673,12 +445,6 @@ section LmapDomain
variable {α' : Type _} {α'' : Type _} (M R)
-/- warning: finsupp.lmap_domain -> Finsupp.lmapDomain is a dubious translation:
-lean 3 declaration is
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/-- Interpret `finsupp.map_domain` as a linear map. -/
def lmapDomain (f : α → α') : (α →₀ M) →ₗ[R] α' →₀ M
where
@@ -687,43 +453,22 @@ def lmapDomain (f : α → α') : (α →₀ M) →ₗ[R] α' →₀ M
map_smul' := mapDomain_smul
#align finsupp.lmap_domain Finsupp.lmapDomain
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@[simp]
theorem lmapDomain_apply (f : α → α') (l : α →₀ M) :
(lmapDomain M R f : (α →₀ M) →ₗ[R] α' →₀ M) l = mapDomain f l :=
rfl
#align finsupp.lmap_domain_apply Finsupp.lmapDomain_apply
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@[simp]
theorem lmapDomain_id : (lmapDomain M R id : (α →₀ M) →ₗ[R] α →₀ M) = LinearMap.id :=
LinearMap.ext fun l => mapDomain_id
#align finsupp.lmap_domain_id Finsupp.lmapDomain_id
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theorem lmapDomain_comp (f : α → α') (g : α' → α'') :
lmapDomain M R (g ∘ f) = (lmapDomain M R g).comp (lmapDomain M R f) :=
LinearMap.ext fun l => mapDomain_comp
#align finsupp.lmap_domain_comp Finsupp.lmapDomain_comp
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-Case conversion may be inaccurate. Consider using '#align finsupp.supported_comap_lmap_domain Finsupp.supported_comap_lmapDomainₓ'. -/
theorem supported_comap_lmapDomain (f : α → α') (s : Set α') :
supported M R (f ⁻¹' s) ≤ (supported M R s).comap (lmapDomain M R f) :=
fun l (hl : ↑l.support ⊆ f ⁻¹' s) =>
@@ -733,9 +478,6 @@ theorem supported_comap_lmapDomain (f : α → α') (s : Set α') :
exact Set.Subset.trans map_domain_support hl
#align finsupp.supported_comap_lmap_domain Finsupp.supported_comap_lmapDomain
-/- warning: finsupp.lmap_domain_supported -> Finsupp.lmapDomain_supported is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.lmap_domain_supported Finsupp.lmapDomain_supportedₓ'. -/
theorem lmapDomain_supported [Nonempty α] (f : α → α') (s : Set α) :
(supported M R s).map (lmapDomain M R f) = supported M R (f '' s) :=
by
@@ -755,12 +497,6 @@ theorem lmapDomain_supported [Nonempty α] (f : α → α') (s : Set α) :
exact Function.invFunOn_eq (by simpa using hl hc)
#align finsupp.lmap_domain_supported Finsupp.lmapDomain_supported
-/- warning: finsupp.lmap_domain_disjoint_ker -> Finsupp.lmapDomain_disjoint_ker is a dubious translation:
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/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a b «expr ∈ » s) -/
theorem lmapDomain_disjoint_ker (f : α → α') {s : Set α}
(H : ∀ (a) (_ : a ∈ s) (b) (_ : b ∈ s), f a = f b → a = b) :
@@ -786,12 +522,6 @@ section LcomapDomain
variable {β : Type _} {R M}
-/- warning: finsupp.lcomap_domain -> Finsupp.lcomapDomain is a dubious translation:
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/-- Given `f : α → β` and a proof `hf` that `f` is injective, `lcomap_domain f hf` is the linear map
sending `l : β →₀ M` to the finitely supported function from `α` to `M` given by composing
`l` with `f`.
@@ -811,12 +541,6 @@ section Total
variable (α) {α' : Type _} (M) {M' : Type _} (R) [AddCommMonoid M'] [Module R M'] (v : α → M)
{v' : α' → M'}
-/- warning: finsupp.total -> Finsupp.total is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align finsupp.total Finsupp.totalₓ'. -/
/-- Interprets (l : α →₀ R) as linear combination of the elements in the family (v : α → M) and
evaluates this linear combination. -/
protected def total : (α →₀ R) →ₗ[R] M :=
@@ -825,54 +549,27 @@ protected def total : (α →₀ R) →ₗ[R] M :=
variable {α M v}
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theorem total_apply (l : α →₀ R) : Finsupp.total α M R v l = l.Sum fun i a => a • v i :=
rfl
#align finsupp.total_apply Finsupp.total_apply
-/- warning: finsupp.total_apply_of_mem_supported -> Finsupp.total_apply_of_mem_supported is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.total_apply_of_mem_supported Finsupp.total_apply_of_mem_supportedₓ'. -/
theorem total_apply_of_mem_supported {l : α →₀ R} {s : Finset α}
(hs : l ∈ supported R R (↑s : Set α)) : Finsupp.total α M R v l = s.Sum fun i => l i • v i :=
Finset.sum_subset hs fun x _ hxg =>
show l x • v x = 0 by rw [not_mem_support_iff.1 hxg, zero_smul]
#align finsupp.total_apply_of_mem_supported Finsupp.total_apply_of_mem_supported
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@[simp]
theorem total_single (c : R) (a : α) : Finsupp.total α M R v (single a c) = c • v a := by
simp [total_apply, sum_single_index]
#align finsupp.total_single Finsupp.total_single
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theorem total_zero_apply (x : α →₀ R) : (Finsupp.total α M R 0) x = 0 := by
simp [Finsupp.total_apply]
#align finsupp.total_zero_apply Finsupp.total_zero_apply
variable (α M)
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@[simp]
theorem total_zero : Finsupp.total α M R 0 = 0 :=
LinearMap.ext (total_zero_apply R)
@@ -880,30 +577,15 @@ theorem total_zero : Finsupp.total α M R 0 = 0 :=
variable {α M}
-/- warning: finsupp.apply_total -> Finsupp.apply_total is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.apply_total Finsupp.apply_totalₓ'. -/
theorem apply_total (f : M →ₗ[R] M') (v) (l : α →₀ R) :
f (Finsupp.total α M R v l) = Finsupp.total α M' R (f ∘ v) l := by
apply Finsupp.induction_linear l <;> simp (config := { contextual := true })
#align finsupp.apply_total Finsupp.apply_total
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-Case conversion may be inaccurate. Consider using '#align finsupp.total_unique Finsupp.total_uniqueₓ'. -/
theorem total_unique [Unique α] (l : α →₀ R) (v) :
Finsupp.total α M R v l = l default • v default := by rw [← total_single, ← unique_single l]
#align finsupp.total_unique Finsupp.total_unique
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theorem total_surjective (h : Function.Surjective v) :
Function.Surjective (Finsupp.total α M R v) :=
by
@@ -912,22 +594,10 @@ theorem total_surjective (h : Function.Surjective v) :
exact ⟨Finsupp.single y 1, by simp [hy]⟩
#align finsupp.total_surjective Finsupp.total_surjective
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theorem total_range (h : Function.Surjective v) : (Finsupp.total α M R v).range = ⊤ :=
range_eq_top.2 <| total_surjective R h
#align finsupp.total_range Finsupp.total_range
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/-- Any module is a quotient of a free module. This is stated as surjectivity of
`finsupp.total M M R id : (M →₀ R) →ₗ[R] M`. -/
theorem total_id_surjective (M) [AddCommMonoid M] [Module R M] :
@@ -935,12 +605,6 @@ theorem total_id_surjective (M) [AddCommMonoid M] [Module R M] :
total_surjective R Function.surjective_id
#align finsupp.total_id_surjective Finsupp.total_id_surjective
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theorem range_total : (Finsupp.total α M R v).range = span R (range v) :=
by
ext x
@@ -959,63 +623,39 @@ theorem range_total : (Finsupp.total α M R v).range = span R (range v) :=
simp [hi]
#align finsupp.range_total Finsupp.range_total
-/- warning: finsupp.lmap_domain_total -> Finsupp.lmapDomain_total is a dubious translation:
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theorem lmapDomain_total (f : α → α') (g : M →ₗ[R] M') (h : ∀ i, g (v i) = v' (f i)) :
(Finsupp.total α' M' R v').comp (lmapDomain R R f) = g.comp (Finsupp.total α M R v) := by
ext l <;> simp [total_apply, Finsupp.sum_mapDomain_index, add_smul, h]
#align finsupp.lmap_domain_total Finsupp.lmapDomain_total
-/- warning: finsupp.total_comp_lmap_domain -> Finsupp.total_comp_lmapDomain is a dubious translation:
-<too large>
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theorem total_comp_lmapDomain (f : α → α') :
(Finsupp.total α' M' R v').comp (Finsupp.lmapDomain R R f) = Finsupp.total α M' R (v' ∘ f) := by
ext; simp
#align finsupp.total_comp_lmap_domain Finsupp.total_comp_lmapDomain
-/- warning: finsupp.total_emb_domain -> Finsupp.total_embDomain is a dubious translation:
-<too large>
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@[simp]
theorem total_embDomain (f : α ↪ α') (l : α →₀ R) :
(Finsupp.total α' M' R v') (embDomain f l) = (Finsupp.total α M' R (v' ∘ f)) l := by
simp [total_apply, Finsupp.sum, support_emb_domain, emb_domain_apply]
#align finsupp.total_emb_domain Finsupp.total_embDomain
-/- warning: finsupp.total_map_domain -> Finsupp.total_mapDomain is a dubious translation:
-<too large>
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@[simp]
theorem total_mapDomain (f : α → α') (l : α →₀ R) :
(Finsupp.total α' M' R v') (mapDomain f l) = (Finsupp.total α M' R (v' ∘ f)) l :=
LinearMap.congr_fun (total_comp_lmapDomain _ _) l
#align finsupp.total_map_domain Finsupp.total_mapDomain
-/- warning: finsupp.total_equiv_map_domain -> Finsupp.total_equivMapDomain is a dubious translation:
-<too large>
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@[simp]
theorem total_equivMapDomain (f : α ≃ α') (l : α →₀ R) :
(Finsupp.total α' M' R v') (equivMapDomain f l) = (Finsupp.total α M' R (v' ∘ f)) l := by
rw [equiv_map_domain_eq_map_domain, total_map_domain]
#align finsupp.total_equiv_map_domain Finsupp.total_equivMapDomain
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/-- A version of `finsupp.range_total` which is useful for going in the other direction -/
theorem span_eq_range_total (s : Set M) : span R s = (Finsupp.total s M R coe).range := by
rw [range_total, Subtype.range_coe_subtype, Set.setOf_mem_eq]
#align finsupp.span_eq_range_total Finsupp.span_eq_range_total
-/- warning: finsupp.mem_span_iff_total -> Finsupp.mem_span_iff_total is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.mem_span_iff_total Finsupp.mem_span_iff_totalₓ'. -/
theorem mem_span_iff_total (s : Set M) (x : M) :
x ∈ span R s ↔ ∃ l : s →₀ R, Finsupp.total s M R coe l = x :=
(SetLike.ext_iff.1 <| span_eq_range_total _ _) x
@@ -1023,12 +663,6 @@ theorem mem_span_iff_total (s : Set M) (x : M) :
variable {R}
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-Case conversion may be inaccurate. Consider using '#align finsupp.mem_span_range_iff_exists_finsupp Finsupp.mem_span_range_iff_exists_finsuppₓ'. -/
theorem mem_span_range_iff_exists_finsupp {v : α → M} {x : M} :
x ∈ span R (range v) ↔ ∃ c : α →₀ R, (c.Sum fun i a => a • v i) = x := by
simp only [← Finsupp.range_total, LinearMap.mem_range, Finsupp.total_apply]
@@ -1036,9 +670,6 @@ theorem mem_span_range_iff_exists_finsupp {v : α → M} {x : M} :
variable (R)
-/- warning: finsupp.span_image_eq_map_total -> Finsupp.span_image_eq_map_total is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.span_image_eq_map_total Finsupp.span_image_eq_map_totalₓ'. -/
theorem span_image_eq_map_total (s : Set α) :
span R (v '' s) = Submodule.map (Finsupp.total α M R v) (supported R R s) :=
by
@@ -1058,26 +689,17 @@ theorem span_image_eq_map_total (s : Set α) :
refine' sum_mem _; simp [this]
#align finsupp.span_image_eq_map_total Finsupp.span_image_eq_map_total
-/- warning: finsupp.mem_span_image_iff_total -> Finsupp.mem_span_image_iff_total is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.mem_span_image_iff_total Finsupp.mem_span_image_iff_totalₓ'. -/
theorem mem_span_image_iff_total {s : Set α} {x : M} :
x ∈ span R (v '' s) ↔ ∃ l ∈ supported R R s, Finsupp.total α M R v l = x := by
rw [span_image_eq_map_total]; simp
#align finsupp.mem_span_image_iff_total Finsupp.mem_span_image_iff_total
-/- warning: finsupp.total_option -> Finsupp.total_option is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.total_option Finsupp.total_optionₓ'. -/
theorem total_option (v : Option α → M) (f : Option α →₀ R) :
Finsupp.total (Option α) M R v f =
f none • v none + Finsupp.total α M R (v ∘ Option.some) f.some :=
by rw [total_apply, sum_option_index_smul, total_apply]
#align finsupp.total_option Finsupp.total_option
-/- warning: finsupp.total_total -> Finsupp.total_total is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.total_total Finsupp.total_totalₓ'. -/
theorem total_total {α β : Type _} (A : α → M) (B : β → α →₀ R) (f : β →₀ R) :
Finsupp.total α M R A (Finsupp.total β (α →₀ R) R B f) =
Finsupp.total β M R (fun b => Finsupp.total α M R A (B b)) f :=
@@ -1090,12 +712,6 @@ theorem total_total {α β : Type _} (A : α → M) (B : β → α →₀ R) (f
· simp [sum_single_index, sum_smul_index, smul_sum, mul_smul]
#align finsupp.total_total Finsupp.total_total
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-Case conversion may be inaccurate. Consider using '#align finsupp.total_fin_zero Finsupp.total_fin_zeroₓ'. -/
@[simp]
theorem total_fin_zero (f : Fin 0 → M) : Finsupp.total (Fin 0) M R f = 0 := by ext i;
apply finZeroElim i
@@ -1103,9 +719,6 @@ theorem total_fin_zero (f : Fin 0 → M) : Finsupp.total (Fin 0) M R f = 0 := by
variable (α) (M) (v)
-/- warning: finsupp.total_on -> Finsupp.totalOn is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.total_on Finsupp.totalOnₓ'. -/
/-- `finsupp.total_on M v s` interprets `p : α →₀ R` as a linear combination of a
subset of the vectors in `v`, mapping it to the span of those vectors.
@@ -1118,9 +731,6 @@ protected def totalOn (s : Set α) : supported R R s →ₗ[R] span R (v '' s) :
variable {α} {M} {v}
-/- warning: finsupp.total_on_range -> Finsupp.totalOn_range is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.total_on_range Finsupp.totalOn_rangeₓ'. -/
theorem totalOn_range (s : Set α) : (Finsupp.totalOn α M R v s).range = ⊤ :=
by
rw [Finsupp.totalOn, LinearMap.range_eq_map, LinearMap.map_codRestrict, ←
@@ -1129,29 +739,17 @@ theorem totalOn_range (s : Set α) : (Finsupp.totalOn α M R v s).range = ⊤ :=
exact (span_image_eq_map_total _ _).le
#align finsupp.total_on_range Finsupp.totalOn_range
-/- warning: finsupp.total_comp -> Finsupp.total_comp is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.total_comp Finsupp.total_compₓ'. -/
theorem total_comp (f : α' → α) :
Finsupp.total α' M R (v ∘ f) = (Finsupp.total α M R v).comp (lmapDomain R R f) := by ext;
simp [total_apply]
#align finsupp.total_comp Finsupp.total_comp
-/- warning: finsupp.total_comap_domain -> Finsupp.total_comapDomain is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.total_comap_domain Finsupp.total_comapDomainₓ'. -/
theorem total_comapDomain (f : α → α') (l : α' →₀ R) (hf : Set.InjOn f (f ⁻¹' ↑l.support)) :
Finsupp.total α M R v (Finsupp.comapDomain f l hf) =
(l.support.Preimage f hf).Sum fun i => l (f i) • v i :=
by rw [Finsupp.total_apply] <;> rfl
#align finsupp.total_comap_domain Finsupp.total_comapDomain
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theorem total_onFinset {s : Finset α} {f : α → R} (g : α → M) (hf : ∀ a, f a ≠ 0 → a ∈ s) :
Finsupp.total α M R g (Finsupp.onFinset s f hf) = Finset.sum s fun x : α => f x • g x :=
by
@@ -1164,12 +762,6 @@ theorem total_onFinset {s : Finset α} {f : α → R} (g : α → M) (hf : ∀ a
end Total
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/-- An equivalence of domains induces a linear equivalence of finitely supported functions.
This is `finsupp.dom_congr` as a `linear_equiv`.
@@ -1179,59 +771,35 @@ protected def domLCongr {α₁ α₂ : Type _} (e : α₁ ≃ α₂) : (α₁
simpa only [equiv_map_domain_eq_map_domain, dom_congr_apply] using (lmap_domain M R e).map_smul
#align finsupp.dom_lcongr Finsupp.domLCongr
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@[simp]
theorem domLCongr_apply {α₁ : Type _} {α₂ : Type _} (e : α₁ ≃ α₂) (v : α₁ →₀ M) :
(Finsupp.domLCongr e : _ ≃ₗ[R] _) v = Finsupp.domCongr e v :=
rfl
#align finsupp.dom_lcongr_apply Finsupp.domLCongr_apply
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@[simp]
theorem domLCongr_refl : Finsupp.domLCongr (Equiv.refl α) = LinearEquiv.refl R (α →₀ M) :=
LinearEquiv.ext fun _ => equivMapDomain_refl _
#align finsupp.dom_lcongr_refl Finsupp.domLCongr_refl
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theorem domLCongr_trans {α₁ α₂ α₃ : Type _} (f : α₁ ≃ α₂) (f₂ : α₂ ≃ α₃) :
(Finsupp.domLCongr f).trans (Finsupp.domLCongr f₂) =
(Finsupp.domLCongr (f.trans f₂) : (_ →₀ M) ≃ₗ[R] _) :=
LinearEquiv.ext fun _ => (equivMapDomain_trans _ _ _).symm
#align finsupp.dom_lcongr_trans Finsupp.domLCongr_trans
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@[simp]
theorem domLCongr_symm {α₁ α₂ : Type _} (f : α₁ ≃ α₂) :
((Finsupp.domLCongr f).symm : (_ →₀ M) ≃ₗ[R] _) = Finsupp.domLCongr f.symm :=
LinearEquiv.ext fun x => rfl
#align finsupp.dom_lcongr_symm Finsupp.domLCongr_symm
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@[simp]
theorem domLCongr_single {α₁ : Type _} {α₂ : Type _} (e : α₁ ≃ α₂) (i : α₁) (m : M) :
(Finsupp.domLCongr e : _ ≃ₗ[R] _) (Finsupp.single i m) = Finsupp.single (e i) m := by
simp [Finsupp.domLCongr, Finsupp.domCongr, equiv_map_domain_single]
#align finsupp.dom_lcongr_single Finsupp.domLCongr_single
-/- warning: finsupp.congr -> Finsupp.congr is a dubious translation:
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/-- An equivalence of sets induces a linear equivalence of `finsupp`s supported on those sets. -/
noncomputable def congr {α' : Type _} (s : Set α) (t : Set α') (e : s ≃ t) :
supported M R s ≃ₗ[R] supported M R t :=
@@ -1242,12 +810,6 @@ noncomputable def congr {α' : Type _} (s : Set α) (t : Set α') (e : s ≃ t)
exact Finsupp.domLCongr e
#align finsupp.congr Finsupp.congr
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/-- `finsupp.map_range` as a `linear_map`. -/
@[simps]
def mapRange.linearMap (f : M →ₗ[R] N) : (α →₀ M) →ₗ[R] α →₀ N :=
@@ -1258,33 +820,18 @@ def mapRange.linearMap (f : M →ₗ[R] N) : (α →₀ M) →ₗ[R] α →₀ N
map_smul' := fun c v => mapRange_smul c v (f.map_smul c) }
#align finsupp.map_range.linear_map Finsupp.mapRange.linearMap
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@[simp]
theorem mapRange.linearMap_id :
mapRange.linearMap LinearMap.id = (LinearMap.id : (α →₀ M) →ₗ[R] _) :=
LinearMap.ext mapRange_id
#align finsupp.map_range.linear_map_id Finsupp.mapRange.linearMap_id
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theorem mapRange.linearMap_comp (f : N →ₗ[R] P) (f₂ : M →ₗ[R] N) :
(mapRange.linearMap (f.comp f₂) : (α →₀ _) →ₗ[R] _) =
(mapRange.linearMap f).comp (mapRange.linearMap f₂) :=
LinearMap.ext <| mapRange_comp _ _ _ _ _
#align finsupp.map_range.linear_map_comp Finsupp.mapRange.linearMap_comp
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@[simp]
theorem mapRange.linearMap_toAddMonoidHom (f : M →ₗ[R] N) :
(mapRange.linearMap f).toAddMonoidHom =
@@ -1292,12 +839,6 @@ theorem mapRange.linearMap_toAddMonoidHom (f : M →ₗ[R] N) :
AddMonoidHom.ext fun _ => rfl
#align finsupp.map_range.linear_map_to_add_monoid_hom Finsupp.mapRange.linearMap_toAddMonoidHom
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/-- `finsupp.map_range` as a `linear_equiv`. -/
@[simps apply]
def mapRange.linearEquiv (e : M ≃ₗ[R] N) : (α →₀ M) ≃ₗ[R] α →₀ N :=
@@ -1307,95 +848,53 @@ def mapRange.linearEquiv (e : M ≃ₗ[R] N) : (α →₀ M) ≃ₗ[R] α →₀
invFun := mapRange e.symm e.symm.map_zero }
#align finsupp.map_range.linear_equiv Finsupp.mapRange.linearEquiv
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@[simp]
theorem mapRange.linearEquiv_refl :
mapRange.linearEquiv (LinearEquiv.refl R M) = LinearEquiv.refl R (α →₀ M) :=
LinearEquiv.ext mapRange_id
#align finsupp.map_range.linear_equiv_refl Finsupp.mapRange.linearEquiv_refl
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-<too large>
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theorem mapRange.linearEquiv_trans (f : M ≃ₗ[R] N) (f₂ : N ≃ₗ[R] P) :
(mapRange.linearEquiv (f.trans f₂) : (α →₀ _) ≃ₗ[R] _) =
(mapRange.linearEquiv f).trans (mapRange.linearEquiv f₂) :=
LinearEquiv.ext <| mapRange_comp _ _ _ _ _
#align finsupp.map_range.linear_equiv_trans Finsupp.mapRange.linearEquiv_trans
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@[simp]
theorem mapRange.linearEquiv_symm (f : M ≃ₗ[R] N) :
((mapRange.linearEquiv f).symm : (α →₀ _) ≃ₗ[R] _) = mapRange.linearEquiv f.symm :=
LinearEquiv.ext fun x => rfl
#align finsupp.map_range.linear_equiv_symm Finsupp.mapRange.linearEquiv_symm
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@[simp]
theorem mapRange.linearEquiv_toAddEquiv (f : M ≃ₗ[R] N) :
(mapRange.linearEquiv f).toAddEquiv = (mapRange.addEquiv f.toAddEquiv : (α →₀ M) ≃+ _) :=
AddEquiv.ext fun _ => rfl
#align finsupp.map_range.linear_equiv_to_add_equiv Finsupp.mapRange.linearEquiv_toAddEquiv
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@[simp]
theorem mapRange.linearEquiv_toLinearMap (f : M ≃ₗ[R] N) :
(mapRange.linearEquiv f).toLinearMap = (mapRange.linearMap f.toLinearMap : (α →₀ M) →ₗ[R] _) :=
LinearMap.ext fun _ => rfl
#align finsupp.map_range.linear_equiv_to_linear_map Finsupp.mapRange.linearEquiv_toLinearMap
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/-- An equivalence of domain and a linear equivalence of codomain induce a linear equivalence of the
corresponding finitely supported functions. -/
def lcongr {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N) : (ι →₀ M) ≃ₗ[R] κ →₀ N :=
(Finsupp.domLCongr e₁).trans (mapRange.linearEquiv e₂)
#align finsupp.lcongr Finsupp.lcongr
-/- warning: finsupp.lcongr_single -> Finsupp.lcongr_single is a dubious translation:
-<too large>
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@[simp]
theorem lcongr_single {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N) (i : ι) (m : M) :
lcongr e₁ e₂ (Finsupp.single i m) = Finsupp.single (e₁ i) (e₂ m) := by simp [lcongr]
#align finsupp.lcongr_single Finsupp.lcongr_single
-/- warning: finsupp.lcongr_apply_apply -> Finsupp.lcongr_apply_apply is a dubious translation:
-<too large>
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@[simp]
theorem lcongr_apply_apply {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N) (f : ι →₀ M) (k : κ) :
lcongr e₁ e₂ f k = e₂ (f (e₁.symm k)) :=
rfl
#align finsupp.lcongr_apply_apply Finsupp.lcongr_apply_apply
-/- warning: finsupp.lcongr_symm_single -> Finsupp.lcongr_symm_single is a dubious translation:
-<too large>
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theorem lcongr_symm_single {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N) (k : κ) (n : N) :
(lcongr e₁ e₂).symm (Finsupp.single k n) = Finsupp.single (e₁.symm k) (e₂.symm n) :=
by
@@ -1403,9 +902,6 @@ theorem lcongr_symm_single {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[
simp
#align finsupp.lcongr_symm_single Finsupp.lcongr_symm_single
-/- warning: finsupp.lcongr_symm -> Finsupp.lcongr_symm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.lcongr_symm Finsupp.lcongr_symmₓ'. -/
@[simp]
theorem lcongr_symm {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N) :
(lcongr e₁ e₂).symm = lcongr e₁.symm e₂.symm := by ext; rfl
@@ -1415,12 +911,6 @@ section Sum
variable (R)
-/- warning: finsupp.sum_finsupp_lequiv_prod_finsupp -> Finsupp.sumFinsuppLEquivProdFinsupp is a dubious translation:
-lean 3 declaration is
- forall {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {α : Type.{u3}} {β : Type.{u4}}, LinearEquiv.{u2, u2, max (max u3 u4) u1, max (max u3 u1) u4 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (Finsupp.{max u3 u4, u1} (Sum.{u3, u4} α β) M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Prod.{max u3 u1, max u4 u1} (Finsupp.{u3, u1} α M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u4, u1} β M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (Finsupp.addCommMonoid.{max u3 u4, u1} (Sum.{u3, u4} α β) M _inst_3) (Prod.addCommMonoid.{max u3 u1, max u4 u1} (Finsupp.{u3, u1} α M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u4, u1} β M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.addCommMonoid.{u3, u1} α M _inst_3) (Finsupp.addCommMonoid.{u4, u1} β M _inst_3)) (Finsupp.module.{max u3 u4, u1, u2} (Sum.{u3, u4} α β) M R _inst_1 _inst_3 _inst_4) (Prod.module.{u2, max u3 u1, max u4 u1} R (Finsupp.{u3, u1} α M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u4, u1} β M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α M _inst_3) (Finsupp.addCommMonoid.{u4, u1} β M _inst_3) (Finsupp.module.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u1, u2} β M R _inst_1 _inst_3 _inst_4))
-but is expected to have type
- forall {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {α : Type.{u3}} {β : Type.{u4}}, LinearEquiv.{u2, u2, max u1 u4 u3, max (max u1 u4) u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (Finsupp.{max u4 u3, u1} (Sum.{u3, u4} α β) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Prod.{max u1 u3, max u1 u4} (Finsupp.{u3, u1} α M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Finsupp.{u4, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.addCommMonoid.{max u3 u4, u1} (Sum.{u3, u4} α β) M _inst_3) (Prod.instAddCommMonoidSum.{max u1 u3, max u1 u4} (Finsupp.{u3, u1} α M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Finsupp.{u4, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Finsupp.addCommMonoid.{u3, u1} α M _inst_3) (Finsupp.addCommMonoid.{u4, u1} β M _inst_3)) (Finsupp.module.{max u3 u4, u1, u2} (Sum.{u3, u4} α β) M R _inst_1 _inst_3 _inst_4) (Prod.module.{u2, max u1 u3, max u1 u4} R (Finsupp.{u3, u1} α M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Finsupp.{u4, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α M _inst_3) (Finsupp.addCommMonoid.{u4, u1} β M _inst_3) (Finsupp.module.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u1, u2} β M R _inst_1 _inst_3 _inst_4))
-Case conversion may be inaccurate. Consider using '#align finsupp.sum_finsupp_lequiv_prod_finsupp Finsupp.sumFinsuppLEquivProdFinsuppₓ'. -/
/-- The linear equivalence between `(α ⊕ β) →₀ M` and `(α →₀ M) × (β →₀ M)`.
This is the `linear_equiv` version of `finsupp.sum_finsupp_equiv_prod_finsupp`. -/
@@ -1434,33 +924,21 @@ def sumFinsuppLEquivProdFinsupp {α β : Type _} : (Sum α β →₀ M) ≃ₗ[R
RingHom.id_apply] }
#align finsupp.sum_finsupp_lequiv_prod_finsupp Finsupp.sumFinsuppLEquivProdFinsupp
-/- warning: finsupp.fst_sum_finsupp_lequiv_prod_finsupp -> Finsupp.fst_sumFinsuppLEquivProdFinsupp is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.fst_sum_finsupp_lequiv_prod_finsupp Finsupp.fst_sumFinsuppLEquivProdFinsuppₓ'. -/
theorem fst_sumFinsuppLEquivProdFinsupp {α β : Type _} (f : Sum α β →₀ M) (x : α) :
(sumFinsuppLEquivProdFinsupp R f).1 x = f (Sum.inl x) :=
rfl
#align finsupp.fst_sum_finsupp_lequiv_prod_finsupp Finsupp.fst_sumFinsuppLEquivProdFinsupp
-/- warning: finsupp.snd_sum_finsupp_lequiv_prod_finsupp -> Finsupp.snd_sumFinsuppLEquivProdFinsupp is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.snd_sum_finsupp_lequiv_prod_finsupp Finsupp.snd_sumFinsuppLEquivProdFinsuppₓ'. -/
theorem snd_sumFinsuppLEquivProdFinsupp {α β : Type _} (f : Sum α β →₀ M) (y : β) :
(sumFinsuppLEquivProdFinsupp R f).2 y = f (Sum.inr y) :=
rfl
#align finsupp.snd_sum_finsupp_lequiv_prod_finsupp Finsupp.snd_sumFinsuppLEquivProdFinsupp
-/- warning: finsupp.sum_finsupp_lequiv_prod_finsupp_symm_inl -> Finsupp.sumFinsuppLEquivProdFinsupp_symm_inl is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.sum_finsupp_lequiv_prod_finsupp_symm_inl Finsupp.sumFinsuppLEquivProdFinsupp_symm_inlₓ'. -/
theorem sumFinsuppLEquivProdFinsupp_symm_inl {α β : Type _} (fg : (α →₀ M) × (β →₀ M)) (x : α) :
((sumFinsuppLEquivProdFinsupp R).symm fg) (Sum.inl x) = fg.1 x :=
rfl
#align finsupp.sum_finsupp_lequiv_prod_finsupp_symm_inl Finsupp.sumFinsuppLEquivProdFinsupp_symm_inl
-/- warning: finsupp.sum_finsupp_lequiv_prod_finsupp_symm_inr -> Finsupp.sumFinsuppLEquivProdFinsupp_symm_inr is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.sum_finsupp_lequiv_prod_finsupp_symm_inr Finsupp.sumFinsuppLEquivProdFinsupp_symm_inrₓ'. -/
theorem sumFinsuppLEquivProdFinsupp_symm_inr {α β : Type _} (fg : (α →₀ M) × (β →₀ M)) (y : β) :
((sumFinsuppLEquivProdFinsupp R).symm fg) (Sum.inr y) = fg.2 y :=
rfl
@@ -1474,12 +952,6 @@ variable {η : Type _} [Fintype η] {ιs : η → Type _} [Zero α]
variable (R)
-/- warning: finsupp.sigma_finsupp_lequiv_pi_finsupp -> Finsupp.sigmaFinsuppLEquivPiFinsupp is a dubious translation:
-lean 3 declaration is
- forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] {η : Type.{u2}} [_inst_9 : Fintype.{u2} η] {M : Type.{u3}} {ιs : η -> Type.{u4}} [_inst_11 : AddCommMonoid.{u3} M] [_inst_12 : Module.{u1, u3} R M _inst_1 _inst_11], LinearEquiv.{u1, u1, max (max u2 u4) u3, max u2 u4 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{max u2 u4, u3} (Sigma.{u2, u4} η (fun (j : η) => ιs j)) M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_11)))) (forall (j : η), Finsupp.{u4, u3} (ιs j) M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_11)))) (Finsupp.addCommMonoid.{max u2 u4, u3} (Sigma.{u2, u4} η (fun (j : η) => ιs j)) M _inst_11) (Pi.addCommMonoid.{u2, max u4 u3} η (fun (j : η) => Finsupp.{u4, u3} (ιs j) M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_11)))) (fun (i : η) => Finsupp.addCommMonoid.{u4, u3} (ιs i) M _inst_11)) (Finsupp.module.{max u2 u4, u3, u1} (Sigma.{u2, u4} η (fun (j : η) => ιs j)) M R _inst_1 _inst_11 _inst_12) (Pi.module.{u2, max u4 u3, u1} η (fun (j : η) => Finsupp.{u4, u3} (ιs j) M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_11)))) R _inst_1 (fun (i : η) => Finsupp.addCommMonoid.{u4, u3} (ιs i) M _inst_11) (fun (i : η) => Finsupp.module.{u4, u3, u1} (ιs i) M R _inst_1 _inst_11 _inst_12))
-but is expected to have type
- forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] {η : Type.{u2}} [_inst_9 : Fintype.{u2} η] {M : Type.{u3}} {ιs : η -> Type.{u4}} [_inst_11 : AddCommMonoid.{u3} M] [_inst_12 : Module.{u1, u3} R M _inst_1 _inst_11], LinearEquiv.{u1, u1, max u3 u4 u2, max (max u2 u3) u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{max u4 u2, u3} (Sigma.{u2, u4} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_11))) (forall (j : η), Finsupp.{u4, u3} (ιs j) M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_11))) (Finsupp.addCommMonoid.{max u2 u4, u3} (Sigma.{u2, u4} η (fun (j : η) => ιs j)) M _inst_11) (Pi.addCommMonoid.{u2, max u3 u4} η (fun (j : η) => Finsupp.{u4, u3} (ιs j) M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_11))) (fun (i : η) => Finsupp.addCommMonoid.{u4, u3} (ιs i) M _inst_11)) (Finsupp.module.{max u2 u4, u3, u1} (Sigma.{u2, u4} η (fun (j : η) => ιs j)) M R _inst_1 _inst_11 _inst_12) (Pi.module.{u2, max u3 u4, u1} η (fun (j : η) => Finsupp.{u4, u3} (ιs j) M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_11))) R _inst_1 (fun (i : η) => Finsupp.addCommMonoid.{u4, u3} (ιs i) M _inst_11) (fun (i : η) => Finsupp.module.{u4, u3, u1} (ιs i) M R _inst_1 _inst_11 _inst_12))
-Case conversion may be inaccurate. Consider using '#align finsupp.sigma_finsupp_lequiv_pi_finsupp Finsupp.sigmaFinsuppLEquivPiFinsuppₓ'. -/
/-- On a `fintype η`, `finsupp.split` is a linear equivalence between
`(Σ (j : η), ιs j) →₀ M` and `Π j, (ιs j →₀ M)`.
@@ -1489,18 +961,12 @@ noncomputable def sigmaFinsuppLEquivPiFinsupp {M : Type _} {ιs : η → Type _}
{ sigmaFinsuppAddEquivPiFinsupp with map_smul' := fun c f => by ext; simp }
#align finsupp.sigma_finsupp_lequiv_pi_finsupp Finsupp.sigmaFinsuppLEquivPiFinsupp
-/- warning: finsupp.sigma_finsupp_lequiv_pi_finsupp_apply -> Finsupp.sigmaFinsuppLEquivPiFinsupp_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.sigma_finsupp_lequiv_pi_finsupp_apply Finsupp.sigmaFinsuppLEquivPiFinsupp_applyₓ'. -/
@[simp]
theorem sigmaFinsuppLEquivPiFinsupp_apply {M : Type _} {ιs : η → Type _} [AddCommMonoid M]
[Module R M] (f : (Σj, ιs j) →₀ M) (j i) : sigmaFinsuppLEquivPiFinsupp R f j i = f ⟨j, i⟩ :=
rfl
#align finsupp.sigma_finsupp_lequiv_pi_finsupp_apply Finsupp.sigmaFinsuppLEquivPiFinsupp_apply
-/- warning: finsupp.sigma_finsupp_lequiv_pi_finsupp_symm_apply -> Finsupp.sigmaFinsuppLEquivPiFinsupp_symm_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.sigma_finsupp_lequiv_pi_finsupp_symm_apply Finsupp.sigmaFinsuppLEquivPiFinsupp_symm_applyₓ'. -/
@[simp]
theorem sigmaFinsuppLEquivPiFinsupp_symm_apply {M : Type _} {ιs : η → Type _} [AddCommMonoid M]
[Module R M] (f : ∀ j, ιs j →₀ M) (ji) :
@@ -1512,12 +978,6 @@ end Sigma
section Prod
-/- warning: finsupp.finsupp_prod_lequiv -> Finsupp.finsuppProdLEquiv is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} (R : Type.{u3}) {M : Type.{u4}} [_inst_9 : Semiring.{u3} R] [_inst_10 : AddCommMonoid.{u4} M] [_inst_11 : Module.{u3, u4} R M _inst_9 _inst_10], LinearEquiv.{u3, u3, max (max u1 u2) u4, max u1 u2 u4} R R _inst_9 _inst_9 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_9)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_9)) (RingHomInvPair.ids.{u3} R _inst_9) (RingHomInvPair.ids.{u3} R _inst_9) (Finsupp.{max u1 u2, u4} (Prod.{u1, u2} α β) M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_10)))) (Finsupp.{u1, max u2 u4} α (Finsupp.{u2, u4} β M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_10)))) (Finsupp.zero.{u2, u4} β M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_10))))) (Finsupp.addCommMonoid.{max u1 u2, u4} (Prod.{u1, u2} α β) M _inst_10) (Finsupp.addCommMonoid.{u1, max u2 u4} α (Finsupp.{u2, u4} β M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_10)))) (Finsupp.addCommMonoid.{u2, u4} β M _inst_10)) (Finsupp.module.{max u1 u2, u4, u3} (Prod.{u1, u2} α β) M R _inst_9 _inst_10 _inst_11) (Finsupp.module.{u1, max u2 u4, u3} α (Finsupp.{u2, u4} β M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_10)))) R _inst_9 (Finsupp.addCommMonoid.{u2, u4} β M _inst_10) (Finsupp.module.{u2, u4, u3} β M R _inst_9 _inst_10 _inst_11))
-but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u2}} (R : Type.{u3}) {M : Type.{u4}} [_inst_9 : Semiring.{u3} R] [_inst_10 : AddCommMonoid.{u4} M] [_inst_11 : Module.{u3, u4} R M _inst_9 _inst_10], LinearEquiv.{u3, u3, max u4 u2 u1, max (max u4 u2) u1} R R _inst_9 _inst_9 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_9)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_9)) (RingHomInvPair.ids.{u3} R _inst_9) (RingHomInvPair.ids.{u3} R _inst_9) (Finsupp.{max u2 u1, u4} (Prod.{u1, u2} α β) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_10))) (Finsupp.{u1, max u4 u2} α (Finsupp.{u2, u4} β M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_10))) (Finsupp.zero.{u2, u4} β M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_10)))) (Finsupp.addCommMonoid.{max u1 u2, u4} (Prod.{u1, u2} α β) M _inst_10) (Finsupp.addCommMonoid.{u1, max u2 u4} α (Finsupp.{u2, u4} β M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_10))) (Finsupp.addCommMonoid.{u2, u4} β M _inst_10)) (Finsupp.module.{max u1 u2, u4, u3} (Prod.{u1, u2} α β) M R _inst_9 _inst_10 _inst_11) (Finsupp.module.{u1, max u2 u4, u3} α (Finsupp.{u2, u4} β M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_10))) R _inst_9 (Finsupp.addCommMonoid.{u2, u4} β M _inst_10) (Finsupp.module.{u2, u4, u3} β M R _inst_9 _inst_10 _inst_11))
-Case conversion may be inaccurate. Consider using '#align finsupp.finsupp_prod_lequiv Finsupp.finsuppProdLEquivₓ'. -/
/-- The linear equivalence between `α × β →₀ M` and `α →₀ β →₀ M`.
This is the `linear_equiv` version of `finsupp.finsupp_prod_equiv`. -/
@@ -1529,18 +989,12 @@ noncomputable def finsuppProdLEquiv {α β : Type _} (R : Type _) {M : Type _} [
map_smul' := fun c f => by ext; simp [finsupp_prod_equiv, curry_apply] }
#align finsupp.finsupp_prod_lequiv Finsupp.finsuppProdLEquiv
-/- warning: finsupp.finsupp_prod_lequiv_apply -> Finsupp.finsuppProdLEquiv_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.finsupp_prod_lequiv_apply Finsupp.finsuppProdLEquiv_applyₓ'. -/
@[simp]
theorem finsuppProdLEquiv_apply {α β R M : Type _} [Semiring R] [AddCommMonoid M] [Module R M]
(f : α × β →₀ M) (x y) : finsuppProdLEquiv R f x y = f (x, y) := by
rw [finsupp_prod_lequiv, LinearEquiv.coe_mk, finsupp_prod_equiv, Finsupp.curry_apply]
#align finsupp.finsupp_prod_lequiv_apply Finsupp.finsuppProdLEquiv_apply
-/- warning: finsupp.finsupp_prod_lequiv_symm_apply -> Finsupp.finsuppProdLEquiv_symm_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.finsupp_prod_lequiv_symm_apply Finsupp.finsuppProdLEquiv_symm_applyₓ'. -/
@[simp]
theorem finsuppProdLEquiv_symm_apply {α β R M : Type _} [Semiring R] [AddCommMonoid M] [Module R M]
(f : α →₀ β →₀ M) (xy) : (finsuppProdLEquiv R).symm f xy = f xy.1 xy.2 := by
@@ -1580,16 +1034,10 @@ protected def Fintype.total : (α → M) →ₗ[S] (α → R) →ₗ[R] M
variable {S}
-/- warning: fintype.total_apply -> Fintype.total_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fintype.total_apply Fintype.total_applyₓ'. -/
theorem Fintype.total_apply (f) : Fintype.total R S v f = ∑ i, f i • v i :=
rfl
#align fintype.total_apply Fintype.total_apply
-/- warning: fintype.total_apply_single -> Fintype.total_apply_single is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fintype.total_apply_single Fintype.total_apply_singleₓ'. -/
@[simp]
theorem Fintype.total_apply_single (i : α) (r : R) :
Fintype.total R S v (Pi.single i r) = r • v i :=
@@ -1600,9 +1048,6 @@ theorem Fintype.total_apply_single (i : α) (r : R) :
variable (S)
-/- warning: finsupp.total_eq_fintype_total_apply -> Finsupp.total_eq_fintype_total_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.total_eq_fintype_total_apply Finsupp.total_eq_fintype_total_applyₓ'. -/
theorem Finsupp.total_eq_fintype_total_apply (x : α → R) :
Finsupp.total α M R v ((Finsupp.linearEquivFunOnFinite R R α).symm x) = Fintype.total R S v x :=
by
@@ -1613,9 +1058,6 @@ theorem Finsupp.total_eq_fintype_total_apply (x : α → R) :
exact zero_smul _ _
#align finsupp.total_eq_fintype_total_apply Finsupp.total_eq_fintype_total_apply
-/- warning: finsupp.total_eq_fintype_total -> Finsupp.total_eq_fintype_total is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finsupp.total_eq_fintype_total Finsupp.total_eq_fintype_totalₓ'. -/
theorem Finsupp.total_eq_fintype_total :
(Finsupp.total α M R v).comp (Finsupp.linearEquivFunOnFinite R R α).symm.toLinearMap =
Fintype.total R S v :=
@@ -1624,9 +1066,6 @@ theorem Finsupp.total_eq_fintype_total :
variable {S}
-/- warning: fintype.range_total -> Fintype.range_total is a dubious translation:
-<too large>
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@[simp]
theorem Fintype.range_total : (Fintype.total R S v).range = Submodule.span R (Set.range v) := by
rw [← Finsupp.total_eq_fintype_total, LinearMap.range_comp, LinearEquiv.toLinearMap_eq_coe,
@@ -1637,12 +1076,6 @@ section SpanRange
variable {v} {x : M}
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/-- An element `x` lies in the span of `v` iff it can be written as sum `∑ cᵢ • vᵢ = x`.
-/
theorem mem_span_range_iff_exists_fun : x ∈ span R (range v) ↔ ∃ c : α → R, (∑ i, c i • v i) = x :=
@@ -1652,12 +1085,6 @@ theorem mem_span_range_iff_exists_fun : x ∈ span R (range v) ↔ ∃ c : α
exact exists_congr fun c => Eq.congr_left <| Finsupp.sum_fintype _ _ fun i => zero_smul _ _
#align mem_span_range_iff_exists_fun mem_span_range_iff_exists_fun
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/-- A family `v : α → V` is generating `V` iff every element `(x : V)`
can be written as sum `∑ cᵢ • vᵢ = x`.
-/
@@ -1680,12 +1107,6 @@ section
variable (R)
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/-- Pick some representation of `x : span R w` as a linear combination in `w`,
using the axiom of choice.
-/
@@ -1693,12 +1114,6 @@ irreducible_def Span.repr (w : Set M) (x : span R w) : w →₀ R :=
((Finsupp.mem_span_iff_total _ _ _).mp x.2).some
#align span.repr Span.repr
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@[simp]
theorem Span.finsupp_total_repr {w : Set M} (x : span R w) :
Finsupp.total w M R coe (Span.repr R w x) = x :=
@@ -1709,31 +1124,16 @@ theorem Span.finsupp_total_repr {w : Set M} (x : span R w) :
end
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protected theorem Submodule.finsupp_sum_mem {ι β : Type _} [Zero β] (S : Submodule R M) (f : ι →₀ β)
(g : ι → β → M) (h : ∀ c, f c ≠ 0 → g c (f c) ∈ S) : f.Sum g ∈ S :=
AddSubmonoidClass.finsupp_sum_mem S f g h
#align submodule.finsupp_sum_mem Submodule.finsupp_sum_mem
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-<too large>
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theorem LinearMap.map_finsupp_total (f : M →ₗ[R] N) {ι : Type _} {g : ι → M} (l : ι →₀ R) :
f (Finsupp.total ι M R g l) = Finsupp.total ι N R (f ∘ g) l := by
simp only [Finsupp.total_apply, Finsupp.total_apply, Finsupp.sum, f.map_sum, f.map_smul]
#align linear_map.map_finsupp_total LinearMap.map_finsupp_total
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theorem Submodule.exists_finset_of_mem_iSup {ι : Sort _} (p : ι → Submodule R M) {m : M}
(hm : m ∈ ⨆ i, p i) : ∃ s : Finset ι, m ∈ ⨆ i ∈ s, p i :=
by
@@ -1744,12 +1144,6 @@ theorem Submodule.exists_finset_of_mem_iSup {ι : Sort _} (p : ι → Submodule
exact this hm
#align submodule.exists_finset_of_mem_supr Submodule.exists_finset_of_mem_iSup
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-Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_iff_exists_finset Submodule.mem_iSup_iff_exists_finsetₓ'. -/
/-- `submodule.exists_finset_of_mem_supr` as an `iff` -/
theorem Submodule.mem_iSup_iff_exists_finset {ι : Sort _} {p : ι → Submodule R M} {m : M} :
(m ∈ ⨆ i, p i) ↔ ∃ s : Finset ι, m ∈ ⨆ i ∈ s, p i :=
@@ -1769,12 +1163,6 @@ theorem mem_span_finset {s : Finset M} {x : M} :
#align mem_span_finset mem_span_finset
-/
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/-- An element `m ∈ M` is contained in the `R`-submodule spanned by a set `s ⊆ M`, if and only if
`m` can be written as a finite `R`-linear combination of elements of `s`.
The implementation uses `finsupp.sum`. -/
@@ -1787,12 +1175,6 @@ theorem mem_span_set {m : M} {s : Set M} :
exact Finsupp.mem_span_image_iff_total R
#align mem_span_set mem_span_set
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/-- If `subsingleton R`, then `M ≃ₗ[R] ι →₀ R` for any type `ι`. -/
@[simps]
def Module.subsingletonEquiv (R M ι : Type _) [Semiring R] [Subsingleton R] [AddCommMonoid M]
@@ -1811,21 +1193,12 @@ variable {R M} {α : Type _}
open Finsupp Function
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-- See also `linear_map.splitting_of_fun_on_fintype_surjective`
/-- A surjective linear map to finitely supported functions has a splitting. -/
def splittingOfFinsuppSurjective (f : M →ₗ[R] α →₀ R) (s : Surjective f) : (α →₀ R) →ₗ[R] M :=
Finsupp.lift _ _ _ fun x : α => (s (Finsupp.single x 1)).some
#align linear_map.splitting_of_finsupp_surjective LinearMap.splittingOfFinsuppSurjective
-/- warning: linear_map.splitting_of_finsupp_surjective_splits -> LinearMap.splittingOfFinsuppSurjective_splits is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_finsupp_surjective_splits LinearMap.splittingOfFinsuppSurjective_splitsₓ'. -/
theorem splittingOfFinsuppSurjective_splits (f : M →ₗ[R] α →₀ R) (s : Surjective f) :
f.comp (splittingOfFinsuppSurjective f s) = LinearMap.id :=
by
@@ -1837,28 +1210,16 @@ theorem splittingOfFinsuppSurjective_splits (f : M →ₗ[R] α →₀ R) (s : S
· rw [zero_smul]
#align linear_map.splitting_of_finsupp_surjective_splits LinearMap.splittingOfFinsuppSurjective_splits
-/- warning: linear_map.left_inverse_splitting_of_finsupp_surjective -> LinearMap.leftInverse_splittingOfFinsuppSurjective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.left_inverse_splitting_of_finsupp_surjective LinearMap.leftInverse_splittingOfFinsuppSurjectiveₓ'. -/
theorem leftInverse_splittingOfFinsuppSurjective (f : M →ₗ[R] α →₀ R) (s : Surjective f) :
LeftInverse f (splittingOfFinsuppSurjective f s) := fun g =>
LinearMap.congr_fun (splittingOfFinsuppSurjective_splits f s) g
#align linear_map.left_inverse_splitting_of_finsupp_surjective LinearMap.leftInverse_splittingOfFinsuppSurjective
-/- warning: linear_map.splitting_of_finsupp_surjective_injective -> LinearMap.splittingOfFinsuppSurjective_injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_finsupp_surjective_injective LinearMap.splittingOfFinsuppSurjective_injectiveₓ'. -/
theorem splittingOfFinsuppSurjective_injective (f : M →ₗ[R] α →₀ R) (s : Surjective f) :
Injective (splittingOfFinsuppSurjective f s) :=
(leftInverse_splittingOfFinsuppSurjective f s).Injective
#align linear_map.splitting_of_finsupp_surjective_injective LinearMap.splittingOfFinsuppSurjective_injective
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-- See also `linear_map.splitting_of_finsupp_surjective`
/-- A surjective linear map to functions on a finite type has a splitting. -/
def splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R) (s : Surjective f) :
@@ -1867,9 +1228,6 @@ def splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R) (s
(linearEquivFunOnFinite R R α).symm.toLinearMap
#align linear_map.splitting_of_fun_on_fintype_surjective LinearMap.splittingOfFunOnFintypeSurjective
-/- warning: linear_map.splitting_of_fun_on_fintype_surjective_splits -> LinearMap.splittingOfFunOnFintypeSurjective_splits is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective_splits LinearMap.splittingOfFunOnFintypeSurjective_splitsₓ'. -/
theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : f.comp (splittingOfFunOnFintypeSurjective f s) = LinearMap.id :=
by
@@ -1880,20 +1238,11 @@ theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R]
rw [zero_smul]
#align linear_map.splitting_of_fun_on_fintype_surjective_splits LinearMap.splittingOfFunOnFintypeSurjective_splits
-/- warning: linear_map.left_inverse_splitting_of_fun_on_fintype_surjective -> LinearMap.leftInverse_splittingOfFunOnFintypeSurjective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.left_inverse_splitting_of_fun_on_fintype_surjective LinearMap.leftInverse_splittingOfFunOnFintypeSurjectiveₓ'. -/
theorem leftInverse_splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : LeftInverse f (splittingOfFunOnFintypeSurjective f s) := fun g =>
LinearMap.congr_fun (splittingOfFunOnFintypeSurjective_splits f s) g
#align linear_map.left_inverse_splitting_of_fun_on_fintype_surjective LinearMap.leftInverse_splittingOfFunOnFintypeSurjective
-/- warning: linear_map.splitting_of_fun_on_fintype_surjective_injective -> LinearMap.splittingOfFunOnFintypeSurjective_injective is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective_injective LinearMap.splittingOfFunOnFintypeSurjective_injectiveₓ'. -/
theorem splittingOfFunOnFintypeSurjective_injective [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : Injective (splittingOfFunOnFintypeSurjective f s) :=
(leftInverse_splittingOfFunOnFintypeSurjective f s).Injective
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -132,12 +132,8 @@ This is the linear version of `finsupp.to_fun`. -/
@[simps]
def lcoeFun : (α →₀ M) →ₗ[R] α → M where
toFun := coeFn
- map_add' x y := by
- ext
- simp
- map_smul' x y := by
- ext
- simp
+ map_add' x y := by ext; simp
+ map_smul' x y := by ext; simp
#align finsupp.lcoe_fun Finsupp.lcoeFun
section LsubtypeDomain
@@ -290,8 +286,7 @@ def supported (s : Set α) : Submodule R (α →₀ M) :=
refine' subset.trans (subset.trans (Finset.coe_subset.2 support_add) _) (union_subset hp hq)
rw [Finset.coe_union]
· simp only [subset_def, Finset.mem_coe, Set.mem_setOf_eq, mem_support_iff, zero_apply]
- intro h ha
- exact (ha rfl).elim
+ intro h ha; exact (ha rfl).elim
· intro a p hp
refine' subset.trans (Finset.coe_subset.2 support_smul) hp
#align finsupp.supported Finsupp.supported
@@ -352,8 +347,7 @@ theorem supported_eq_span_single (s : Set α) :
supported R R s = span R ((fun i => single i 1) '' s) :=
by
refine' (span_eq_of_le _ _ (SetLike.le_def.2 fun l hl => _)).symm
- · rintro _ ⟨_, hp, rfl⟩
- exact single_mem_supported R 1 hp
+ · rintro _ ⟨_, hp, rfl⟩; exact single_mem_supported R 1 hp
· rw [← l.sum_single]
refine' sum_mem fun i il => _
convert@smul_mem R (α →₀ R) _ _ _ _ (single i 1) (l i) _
@@ -461,8 +455,7 @@ theorem supported_iUnion {δ : Type _} (s : δ → Set α) :
rwa [LinearMap.range_comp, range_restrict_dom, Submodule.map_top, range_subtype] at this
rw [range_le_iff_comap, eq_top_iff]
rintro l ⟨⟩
- apply Finsupp.induction l
- · exact zero_mem _
+ apply Finsupp.induction l; · exact zero_mem _
refine' fun x a l hl a0 => add_mem _
by_cases ∃ i, x ∈ s i <;> simp [h]
· cases' h with i hi
@@ -566,18 +559,10 @@ def lsum : (α → M →ₗ[R] N) ≃ₗ[S] (α →₀ M) →ₗ[R] N
map_add' := (liftAddHom fun x => (F x).toAddMonoidHom).map_add
map_smul' := fun c f => by simp [sum_smul_index', smul_sum] }
invFun F x := F.comp (lsingle x)
- left_inv F := by
- ext (x y)
- simp
- right_inv F := by
- ext (x y)
- simp
- map_add' F G := by
- ext (x y)
- simp
- map_smul' F G := by
- ext (x y)
- simp
+ left_inv F := by ext (x y); simp
+ right_inv F := by ext (x y); simp
+ map_add' F G := by ext (x y); simp
+ map_smul' F G := by ext (x y); simp
#align finsupp.lsum Finsupp.lsum
/- warning: finsupp.coe_lsum -> Finsupp.coe_lsum is a dubious translation:
@@ -787,17 +772,12 @@ theorem lmapDomain_disjoint_ker (f : α → α') {s : Set α}
simp; ext x
haveI := Classical.decPred fun x => x ∈ s
by_cases xs : x ∈ s
- · have : Finsupp.sum l (fun a => Finsupp.single (f a)) (f x) = 0 :=
- by
- rw [h₂]
- rfl
+ · have : Finsupp.sum l (fun a => Finsupp.single (f a)) (f x) = 0 := by rw [h₂]; rfl
rw [Finsupp.sum_apply, Finsupp.sum, Finset.sum_eq_single x] at this
· simpa [Finsupp.single_apply]
- · intro y hy xy
- simp [mt (H _ (h₁ hy) _ xs) xy]
+ · intro y hy xy; simp [mt (H _ (h₁ hy) _ xs) xy]
· simp (config := { contextual := true })
- · by_contra h
- exact xs (h₁ <| Finsupp.mem_support_iff.2 h)
+ · by_contra h; exact xs (h₁ <| Finsupp.mem_support_iff.2 h)
#align finsupp.lmap_domain_disjoint_ker Finsupp.lmapDomain_disjoint_ker
end LmapDomain
@@ -820,12 +800,8 @@ This is the linear version of `finsupp.comap_domain`. -/
def lcomapDomain (f : α → β) (hf : Function.Injective f) : (β →₀ M) →ₗ[R] α →₀ M
where
toFun l := Finsupp.comapDomain f l (hf.InjOn _)
- map_add' x y := by
- ext
- simp
- map_smul' c x := by
- ext
- simp
+ map_add' x y := by ext; simp
+ map_smul' c x := by ext; simp
#align finsupp.lcomap_domain Finsupp.lcomapDomain
end LcomapDomain
@@ -995,10 +971,8 @@ theorem lmapDomain_total (f : α → α') (g : M →ₗ[R] M') (h : ∀ i, g (v
<too large>
Case conversion may be inaccurate. Consider using '#align finsupp.total_comp_lmap_domain Finsupp.total_comp_lmapDomainₓ'. -/
theorem total_comp_lmapDomain (f : α → α') :
- (Finsupp.total α' M' R v').comp (Finsupp.lmapDomain R R f) = Finsupp.total α M' R (v' ∘ f) :=
- by
- ext
- simp
+ (Finsupp.total α' M' R v').comp (Finsupp.lmapDomain R R f) = Finsupp.total α M' R (v' ∘ f) := by
+ ext; simp
#align finsupp.total_comp_lmap_domain Finsupp.total_comp_lmapDomain
/- warning: finsupp.total_emb_domain -> Finsupp.total_embDomain is a dubious translation:
@@ -1081,18 +1055,15 @@ theorem span_image_eq_map_total (s : Set α) :
by_cases c ∈ s
· exact smul_mem _ _ (subset_span (Set.mem_image_of_mem _ h))
· simp [(Finsupp.mem_supported' R _).1 hz _ h]
- refine' sum_mem _
- simp [this]
+ refine' sum_mem _; simp [this]
#align finsupp.span_image_eq_map_total Finsupp.span_image_eq_map_total
/- warning: finsupp.mem_span_image_iff_total -> Finsupp.mem_span_image_iff_total is a dubious translation:
<too large>
Case conversion may be inaccurate. Consider using '#align finsupp.mem_span_image_iff_total Finsupp.mem_span_image_iff_totalₓ'. -/
theorem mem_span_image_iff_total {s : Set α} {x : M} :
- x ∈ span R (v '' s) ↔ ∃ l ∈ supported R R s, Finsupp.total α M R v l = x :=
- by
- rw [span_image_eq_map_total]
- simp
+ x ∈ span R (v '' s) ↔ ∃ l ∈ supported R R s, Finsupp.total α M R v l = x := by
+ rw [span_image_eq_map_total]; simp
#align finsupp.mem_span_image_iff_total Finsupp.mem_span_image_iff_total
/- warning: finsupp.total_option -> Finsupp.total_option is a dubious translation:
@@ -1126,9 +1097,7 @@ but is expected to have type
forall {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (f : (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> M), Eq.{max (succ u2) (succ u1)} (LinearMap.{u1, u1, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.total.{0, u2, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) M R _inst_1 _inst_3 _inst_4 f) (OfNat.ofNat.{max u2 u1} (LinearMap.{u1, u1, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) 0 (Zero.toOfNat0.{max u2 u1} (LinearMap.{u1, u1, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (LinearMap.instZeroLinearMap.{u1, u1, u1, u2} R R (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))
Case conversion may be inaccurate. Consider using '#align finsupp.total_fin_zero Finsupp.total_fin_zeroₓ'. -/
@[simp]
-theorem total_fin_zero (f : Fin 0 → M) : Finsupp.total (Fin 0) M R f = 0 :=
- by
- ext i
+theorem total_fin_zero (f : Fin 0 → M) : Finsupp.total (Fin 0) M R f = 0 := by ext i;
apply finZeroElim i
#align finsupp.total_fin_zero Finsupp.total_fin_zero
@@ -1164,9 +1133,7 @@ theorem totalOn_range (s : Set α) : (Finsupp.totalOn α M R v s).range = ⊤ :=
<too large>
Case conversion may be inaccurate. Consider using '#align finsupp.total_comp Finsupp.total_compₓ'. -/
theorem total_comp (f : α' → α) :
- Finsupp.total α' M R (v ∘ f) = (Finsupp.total α M R v).comp (lmapDomain R R f) :=
- by
- ext
+ Finsupp.total α' M R (v ∘ f) = (Finsupp.total α M R v).comp (lmapDomain R R f) := by ext;
simp [total_apply]
#align finsupp.total_comp Finsupp.total_comp
@@ -1441,10 +1408,7 @@ theorem lcongr_symm_single {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[
Case conversion may be inaccurate. Consider using '#align finsupp.lcongr_symm Finsupp.lcongr_symmₓ'. -/
@[simp]
theorem lcongr_symm {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N) :
- (lcongr e₁ e₂).symm = lcongr e₁.symm e₂.symm :=
- by
- ext
- rfl
+ (lcongr e₁ e₂).symm = lcongr e₁.symm e₂.symm := by ext; rfl
#align finsupp.lcongr_symm Finsupp.lcongr_symm
section Sum
@@ -1463,8 +1427,7 @@ This is the `linear_equiv` version of `finsupp.sum_finsupp_equiv_prod_finsupp`.
@[simps apply symm_apply]
def sumFinsuppLEquivProdFinsupp {α β : Type _} : (Sum α β →₀ M) ≃ₗ[R] (α →₀ M) × (β →₀ M) :=
{ sumFinsuppAddEquivProdFinsupp with
- map_smul' := by
- intros
+ map_smul' := by intros ;
ext <;>
simp only [[anonymous], Prod.smul_fst, Prod.smul_snd, smul_apply,
snd_sum_finsupp_add_equiv_prod_finsupp, fst_sum_finsupp_add_equiv_prod_finsupp,
@@ -1523,10 +1486,7 @@ Case conversion may be inaccurate. Consider using '#align finsupp.sigma_finsupp_
This is the `linear_equiv` version of `finsupp.sigma_finsupp_add_equiv_pi_finsupp`. -/
noncomputable def sigmaFinsuppLEquivPiFinsupp {M : Type _} {ιs : η → Type _} [AddCommMonoid M]
[Module R M] : ((Σj, ιs j) →₀ M) ≃ₗ[R] ∀ j, ιs j →₀ M :=
- { sigmaFinsuppAddEquivPiFinsupp with
- map_smul' := fun c f => by
- ext
- simp }
+ { sigmaFinsuppAddEquivPiFinsupp with map_smul' := fun c f => by ext; simp }
#align finsupp.sigma_finsupp_lequiv_pi_finsupp Finsupp.sigmaFinsuppLEquivPiFinsupp
/- warning: finsupp.sigma_finsupp_lequiv_pi_finsupp_apply -> Finsupp.sigmaFinsuppLEquivPiFinsupp_apply is a dubious translation:
@@ -1565,12 +1525,8 @@ noncomputable def finsuppProdLEquiv {α β : Type _} (R : Type _) {M : Type _} [
[AddCommMonoid M] [Module R M] : (α × β →₀ M) ≃ₗ[R] α →₀ β →₀ M :=
{
finsuppProdEquiv with
- map_add' := fun f g => by
- ext
- simp [finsupp_prod_equiv, curry_apply]
- map_smul' := fun c f => by
- ext
- simp [finsupp_prod_equiv, curry_apply] }
+ map_add' := fun f g => by ext; simp [finsupp_prod_equiv, curry_apply]
+ map_smul' := fun c f => by ext; simp [finsupp_prod_equiv, curry_apply] }
#align finsupp.finsupp_prod_lequiv Finsupp.finsuppProdLEquiv
/- warning: finsupp.finsupp_prod_lequiv_apply -> Finsupp.finsuppProdLEquiv_apply is a dubious translation:
@@ -1615,18 +1571,10 @@ protected def Fintype.total : (α → M) →ₗ[S] (α → R) →ₗ[R] M
where
toFun v :=
{ toFun := fun f => ∑ i, f i • v i
- map_add' := fun f g => by
- simp_rw [← Finset.sum_add_distrib, ← add_smul]
- rfl
- map_smul' := fun r f => by
- simp_rw [Finset.smul_sum, smul_smul]
- rfl }
- map_add' u v := by
- ext
- simp [Finset.sum_add_distrib, Pi.add_apply, smul_add]
- map_smul' r v := by
- ext
- simp [Finset.smul_sum, smul_comm _ r]
+ map_add' := fun f g => by simp_rw [← Finset.sum_add_distrib, ← add_smul]; rfl
+ map_smul' := fun r f => by simp_rw [Finset.smul_sum, smul_smul]; rfl }
+ map_add' u v := by ext; simp [Finset.sum_add_distrib, Pi.add_apply, smul_add]
+ map_smul' r v := by ext; simp [Finset.smul_sum, smul_comm _ r]
#align fintype.total Fintype.total
-/
@@ -1851,9 +1799,7 @@ def Module.subsingletonEquiv (R M ι : Type _) [Semiring R] [Subsingleton R] [Ad
[Module R M] : M ≃ₗ[R] ι →₀ R where
toFun m := 0
invFun f := 0
- left_inv m := by
- letI := Module.subsingleton R M
- simp only [eq_iff_true_of_subsingleton]
+ left_inv m := by letI := Module.subsingleton R M; simp only [eq_iff_true_of_subsingleton]
right_inv f := by simp only [eq_iff_true_of_subsingleton]
map_add' m n := (add_zero 0).symm
map_smul' r m := (smul_zero r).symm
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -88,10 +88,7 @@ def lsingle (a : α) : M →ₗ[R] α →₀ M :=
#align finsupp.lsingle Finsupp.lsingle
/- warning: finsupp.lhom_ext -> Finsupp.lhom_ext is a dubious translation:
-lean 3 declaration is
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Case conversion may be inaccurate. Consider using '#align finsupp.lhom_ext Finsupp.lhom_extₓ'. -/
/-- Two `R`-linear maps from `finsupp X M` which agree on each `single x y` agree everywhere. -/
theorem lhom_ext ⦃φ ψ : (α →₀ M) →ₗ[R] N⦄ (h : ∀ a b, φ (single a b) = ψ (single a b)) : φ = ψ :=
@@ -99,10 +96,7 @@ theorem lhom_ext ⦃φ ψ : (α →₀ M) →ₗ[R] N⦄ (h : ∀ a b, φ (singl
#align finsupp.lhom_ext Finsupp.lhom_ext
/- warning: finsupp.lhom_ext' -> Finsupp.lhom_ext' is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align finsupp.lhom_ext' Finsupp.lhom_ext'ₓ'. -/
/-- Two `R`-linear maps from `finsupp X M` which agree on each `single x y` agree everywhere.
@@ -211,10 +205,7 @@ theorem ker_lsingle (a : α) : (lsingle a : M →ₗ[R] α →₀ M).ker = ⊥ :
#align finsupp.ker_lsingle Finsupp.ker_lsingle
/- warning: finsupp.lsingle_range_le_ker_lapply -> Finsupp.lsingle_range_le_ker_lapply is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α) (t : Set.{u1} α), (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) s t) -> (LE.le.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toHasLe.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))))) (iSup.{max u1 u2, succ u1} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => iSup.{max u1 u2, 0} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LinearMap.range.{u3, u3, u2, max u1 u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u3, u3, u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R _inst_1) (Finsupp.lsingle.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a)))) (iInf.{max u1 u2, succ u1} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasInf.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) α (fun (a : α) => iInf.{max u1 u2, 0} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasInf.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a t) => LinearMap.ker.{u3, u3, max u1 u2, u2, max u1 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4) (LinearMap.semilinearMapClass.{u3, u3, max u1 u2, u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lapply.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a)))))
-but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (t : Set.{u3} α), (Disjoint.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} α) (Preorder.toLE.{u3} (Set.{u3} α) (PartialOrder.toPreorder.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) s t) -> (LE.le.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toLE.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))))) (iSup.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => iSup.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) (fun (H : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a)))) (iInf.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) α (fun (a : α) => iInf.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a t) (fun (H : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a t) => LinearMap.ker.{u1, u1, max u3 u2, u2, max u3 u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4) (LinearMap.semilinearMapClass.{u1, u1, max u3 u2, u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lapply.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a)))))
+<too large>
Case conversion may be inaccurate. Consider using '#align finsupp.lsingle_range_le_ker_lapply Finsupp.lsingle_range_le_ker_lapplyₓ'. -/
theorem lsingle_range_le_ker_lapply (s t : Set α) (h : Disjoint s t) :
(⨆ a ∈ s, (lsingle a : M →ₗ[R] α →₀ M).range) ≤ ⨅ a ∈ t, ker (lapply a : (α →₀ M) →ₗ[R] M) :=
@@ -252,10 +243,7 @@ theorem iSup_lsingle_range : (⨆ a, (lsingle a : M →ₗ[R] α →₀ M).range
#align finsupp.supr_lsingle_range Finsupp.iSup_lsingle_range
/- warning: finsupp.disjoint_lsingle_lsingle -> Finsupp.disjoint_lsingle_lsingle is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α) (t : Set.{u1} α), (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) s t) -> (Disjoint.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) (Submodule.orderBot.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (iSup.{max u1 u2, succ u1} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => iSup.{max u1 u2, 0} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LinearMap.range.{u3, u3, u2, max u1 u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u3, u3, u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R _inst_1) (Finsupp.lsingle.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a)))) (iSup.{max u1 u2, succ u1} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => iSup.{max u1 u2, 0} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a t) => LinearMap.range.{u3, u3, u2, max u1 u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u3, u3, u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R _inst_1) (Finsupp.lsingle.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a)))))
-but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (t : Set.{u3} α), (Disjoint.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} α) (Preorder.toLE.{u3} (Set.{u3} α) (PartialOrder.toPreorder.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) s t) -> (Disjoint.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (iSup.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => iSup.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) (fun (H : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a)))) (iSup.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => iSup.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a t) (fun (H : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a t) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a)))))
+<too large>
Case conversion may be inaccurate. Consider using '#align finsupp.disjoint_lsingle_lsingle Finsupp.disjoint_lsingle_lsingleₓ'. -/
theorem disjoint_lsingle_lsingle (s t : Set α) (hs : Disjoint s t) :
Disjoint (⨆ a ∈ s, (lsingle a : M →ₗ[R] α →₀ M).range)
@@ -396,10 +384,7 @@ variable {M R}
section
/- warning: finsupp.restrict_dom_apply -> Finsupp.restrictDom_apply is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α) (l : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))), Eq.{max (succ u1) (succ u2)} (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) ((fun (a : Type.{max u1 u2}) (b : Sort.{max (succ u1) (succ u2)}) [self : HasLiftT.{succ (max u1 u2), max (succ u1) (succ u2)} a b] => self.0) (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (HasLiftT.mk.{succ (max u1 u2), max (succ u1) (succ u2)} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (CoeTCₓ.coe.{succ (max u1 u2), max (succ u1) (succ u2)} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M 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+<too large>
Case conversion may be inaccurate. Consider using '#align finsupp.restrict_dom_apply Finsupp.restrictDom_applyₓ'. -/
@[simp]
theorem restrictDom_apply (s : Set α) (l : α →₀ M) :
@@ -410,10 +395,7 @@ theorem restrictDom_apply (s : Set α) (l : α →₀ M) :
end
/- warning: finsupp.restrict_dom_comp_subtype -> Finsupp.restrictDom_comp_subtype is a dubious translation:
-lean 3 declaration is
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+<too large>
Case conversion may be inaccurate. Consider using '#align finsupp.restrict_dom_comp_subtype Finsupp.restrictDom_comp_subtypeₓ'. -/
theorem restrictDom_comp_subtype (s : Set α) :
(restrictDom M R s).comp (Submodule.subtype _) = LinearMap.id :=
@@ -424,10 +406,7 @@ theorem restrictDom_comp_subtype (s : Set α) :
#align finsupp.restrict_dom_comp_subtype Finsupp.restrictDom_comp_subtype
/- warning: finsupp.range_restrict_dom -> Finsupp.range_restrictDom is a dubious translation:
-lean 3 declaration is
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- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α), Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u3 u2} R (Subtype.{succ (max u3 u2)} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u3 u2, max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) 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+<too large>
Case conversion may be inaccurate. Consider using '#align finsupp.range_restrict_dom Finsupp.range_restrictDomₓ'. -/
theorem range_restrictDom (s : Set α) : (restrictDom M R s).range = ⊤ :=
range_eq_top.2 <|
@@ -573,10 +552,7 @@ section Lsum
variable (S) [Module S N] [SMulCommClass R S N]
/- warning: finsupp.lsum -> Finsupp.lsum is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toHasSmul.{u4, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u4, u3} R N (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u5, u3} S N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u5, u3} S N (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))], LinearEquiv.{u5, u5, max u1 u2 u3, max (max u1 u2) u3} S S _inst_2 _inst_2 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2) (α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u1, max u2 u3} α (fun (ᾰ : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.Function.module.{u1, u5, max u2 u3} α S (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.module.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.module.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)
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- forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toSMul.{u4, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u4, u3} R N (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u5, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} S N (MonoidWithZero.toZero.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))], LinearEquiv.{u5, u5, max (max u1 u2) u3, max u3 u2 u1} S S _inst_2 _inst_2 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2) (α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u4, u4, max u2 u1, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u1, max u2 u3} α (fun (ᾰ : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.module.{u1, max u2 u3, u5} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)
+<too large>
Case conversion may be inaccurate. Consider using '#align finsupp.lsum Finsupp.lsumₓ'. -/
/-- Lift a family of linear maps `M →ₗ[R] N` indexed by `x : α` to a linear map from `α →₀ M` to
`N` using `finsupp.sum`. This is an upgraded version of `finsupp.lift_add_hom`.
@@ -605,10 +581,7 @@ def lsum : (α → M →ₗ[R] N) ≃ₗ[S] (α →₀ M) →ₗ[R] N
#align finsupp.lsum Finsupp.lsum
/- warning: finsupp.coe_lsum -> Finsupp.coe_lsum is a dubious translation:
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(AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u5, u3} S N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u5, u3} S N (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N 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LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) 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_inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f i)))
+<too large>
Case conversion may be inaccurate. Consider using '#align finsupp.coe_lsum Finsupp.coe_lsumₓ'. -/
@[simp]
theorem coe_lsum (f : α → M →ₗ[R] N) : (lsum S f : (α →₀ M) → N) = fun d => d.Sum fun i => f i :=
@@ -616,20 +589,14 @@ theorem coe_lsum (f : α → M →ₗ[R] N) : (lsum S f : (α →₀ M) → N) =
#align finsupp.coe_lsum Finsupp.coe_lsum
/- warning: finsupp.lsum_apply -> Finsupp.lsum_apply is a dubious translation:
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_inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) 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(Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 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+<too large>
Case conversion may be inaccurate. Consider using '#align finsupp.lsum_apply Finsupp.lsum_applyₓ'. -/
theorem lsum_apply (f : α → M →ₗ[R] N) (l : α →₀ M) : Finsupp.lsum S f l = l.Sum fun b => f b :=
rfl
#align finsupp.lsum_apply Finsupp.lsum_apply
/- warning: finsupp.lsum_single -> Finsupp.lsum_single is a dubious translation:
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(Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) 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u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 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_inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) 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+<too large>
Case conversion may be inaccurate. Consider using '#align finsupp.lsum_single Finsupp.lsum_singleₓ'. -/
theorem lsum_single (f : α → M →ₗ[R] N) (i : α) (m : M) :
Finsupp.lsum S f (Finsupp.single i m) = f i m :=
@@ -637,10 +604,7 @@ theorem lsum_single (f : α → M →ₗ[R] N) (i : α) (m : M) :
#align finsupp.lsum_single Finsupp.lsum_single
/- warning: finsupp.lsum_symm_apply -> Finsupp.lsum_symm_apply is a dubious translation:
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(AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u5, u3} S N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u5, u3} S N (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))] (f : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) 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(AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (fun (_x : LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) => α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _x) (SMulHomClass.toFunLike.{max (max u2 u4) u3, u1, max (max u2 u4) u3, max (max u2 u4) u3} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (SMulZeroClass.toSMul.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (SMulZeroClass.toSMul.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u4) u3, u1, max (max u2 u4) u3, max (max u2 u4) u3} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u2 u4) u3, max (max u2 u4) u3, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 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+<too large>
Case conversion may be inaccurate. Consider using '#align finsupp.lsum_symm_apply Finsupp.lsum_symm_applyₓ'. -/
theorem lsum_symm_apply (f : (α →₀ M) →ₗ[R] N) (x : α) : (lsum S).symm f x = f.comp (lsingle x) :=
rfl
@@ -667,10 +631,7 @@ noncomputable def lift : (X → M) ≃+ ((X →₀ R) →ₗ[R] M) :=
#align finsupp.lift Finsupp.lift
/- warning: finsupp.lift_symm_apply -> Finsupp.lift_symm_apply is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align finsupp.lift_symm_apply Finsupp.lift_symm_applyₓ'. -/
@[simp]
theorem lift_symm_apply (f) (x) : ((lift M R X).symm f) x = f (single x 1) :=
@@ -678,10 +639,7 @@ theorem lift_symm_apply (f) (x) : ((lift M R X).symm f) x = f (single x 1) :=
#align finsupp.lift_symm_apply Finsupp.lift_symm_apply
/- warning: finsupp.lift_apply -> Finsupp.lift_apply is a dubious translation:
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (Finsupp.lift.{u1, u2, u3} M R _inst_1 _inst_3 _inst_4 X) f) g) (Finsupp.sum.{u3, u2, u1} X R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) _inst_3 g (fun (x : X) (r : R) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4))))) r (f x)))
+<too large>
Case conversion may be inaccurate. Consider using '#align finsupp.lift_apply Finsupp.lift_applyₓ'. -/
@[simp]
theorem lift_apply (f) (g) : ((lift M R X) f) g = g.Sum fun x r => r • f x :=
@@ -708,10 +666,7 @@ noncomputable def llift : (X → M) ≃ₗ[S] (X →₀ R) →ₗ[R] M :=
#align finsupp.llift Finsupp.llift
/- warning: finsupp.llift_apply -> Finsupp.llift_apply is a dubious translation:
-lean 3 declaration is
- forall (M : Type.{u1}) (R : Type.{u2}) (S : Type.{u3}) [_inst_1 : Semiring.{u2} R] [_inst_2 : Semiring.{u3} S] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u4}) [_inst_9 : Module.{u3, u1} S M _inst_2 _inst_3] [_inst_10 : SMulCommClass.{u2, u3, u1} R S M (SMulZeroClass.toHasSmul.{u2, u1} R M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u1} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u3, u1} S M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u1} S M (MulZeroClass.toHasZero.{u3} S (MulZeroOneClass.toMulZeroClass.{u3} S (MonoidWithZero.toMulZeroOneClass.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)))) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u1} S M (Semiring.toMonoidWithZero.{u3} S _inst_2) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Module.toMulActionWithZero.{u3, u1} S M _inst_2 _inst_3 _inst_9))))] (f : X -> M) (x : Finsupp.{u4, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))), Eq.{succ u1} M 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R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u3) u4} S (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddMonoid.toAddZeroClass.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u3) u4} S (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u2 u3) u4} S (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) _inst_2 (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u3 u4, u2} R R S (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u3) u4, u1, max u2 u4, max (max u2 u3) u4} (LinearEquiv.{u1, u1, max u2 u4, max u2 u3 u4} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u4, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u3 u4, u2} R R S (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max u2 u4} (X -> M) (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Module.toDistribMulAction.{u1, max u2 u4} S (X -> M) _inst_2 (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (Pi.module.{u4, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9))) (Module.toDistribMulAction.{u1, max (max u2 u3) u4} S (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) _inst_2 (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u3 u4, u2} R R S (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max u2 u4, max (max u2 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+<too large>
Case conversion may be inaccurate. Consider using '#align finsupp.llift_apply Finsupp.llift_applyₓ'. -/
@[simp]
theorem llift_apply (f : X → M) (x : X →₀ R) : llift M R S X f x = lift M R X f x :=
@@ -719,10 +674,7 @@ theorem llift_apply (f : X → M) (x : X →₀ R) : llift M R S X f x = lift M
#align finsupp.llift_apply Finsupp.llift_apply
/- warning: finsupp.llift_symm_apply -> Finsupp.llift_symm_apply is a dubious translation:
-lean 3 declaration is
- forall (M : Type.{u1}) (R : Type.{u2}) (S : Type.{u3}) [_inst_1 : Semiring.{u2} R] [_inst_2 : Semiring.{u3} S] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u4}) [_inst_9 : Module.{u3, u1} S M _inst_2 _inst_3] [_inst_10 : SMulCommClass.{u2, u3, u1} R S M (SMulZeroClass.toHasSmul.{u2, u1} R M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u1} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u3, u1} S M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u1} S M (MulZeroClass.toHasZero.{u3} S (MulZeroOneClass.toMulZeroClass.{u3} S (MonoidWithZero.toMulZeroOneClass.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)))) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u1} S M (Semiring.toMonoidWithZero.{u3} S _inst_2) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Module.toMulActionWithZero.{u3, u1} S M _inst_2 _inst_3 _inst_9))))] (f : LinearMap.{u2, u2, max u4 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u4, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u4, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (x : X), Eq.{succ u1} M (coeFn.{max (succ (max (max u4 u2) u1)) (succ (max u4 u1)), max (succ (max (max u4 u2) u1)) (succ (max u4 u1))} (LinearEquiv.{u3, u3, max (max u4 u2) u1, max u4 u1} S S _inst_2 _inst_2 (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2)) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2)) (RingHomInvPair.ids.{u3} S _inst_2) (RingHomInvPair.ids.{u3} S _inst_2) (LinearMap.{u2, u2, max u4 u2, u1} R R _inst_1 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(Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} S M (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u1, u2} S M _inst_2 _inst_3 _inst_9))))] (f : LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (x : X), Eq.{succ u2} M (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u3)} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u2 u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (X -> M) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u1, max u4 u3, u2} R R S (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9))) (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) => X -> M) _x) (SMulHomClass.toFunLike.{max (max u2 u4) u3, u1, max (max u2 u4) u3, max u2 u3} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u2 u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (X -> M) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u1, max u4 u3, u2} R R S (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9))) S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (X -> M) (SMulZeroClass.toSMul.{u1, max (max u2 u4) u3} S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (AddMonoid.toZero.{max (max u2 u4) u3} (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} 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max (max u2 u4) u3} S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (AddMonoid.toAddZeroClass.{max (max u2 u4) u3} (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u4) u3} S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) _inst_2 (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u1, max u4 u3, u2} R R S (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (SMulZeroClass.toSMul.{u1, max u2 u3} S (X -> M) (AddMonoid.toZero.{max u2 u3} (X -> M) (AddCommMonoid.toAddMonoid.{max u2 u3} (X -> M) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)))) (DistribSMul.toSMulZeroClass.{u1, max u2 u3} S (X -> M) (AddMonoid.toAddZeroClass.{max u2 u3} (X -> M) (AddCommMonoid.toAddMonoid.{max u2 u3} (X -> M) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)))) (DistribMulAction.toDistribSMul.{u1, max u2 u3} S (X -> M) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max u2 u3} (X -> M) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3))) (Module.toDistribMulAction.{u1, max u2 u3} S (X -> M) _inst_2 (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (Pi.module.{u3, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u4) u3, u1, max (max u2 u4) u3, max u2 u3} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u2 u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (X -> M) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u1, max u4 u3, u2} R R S (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9))) S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (X -> M) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u3} (X -> M) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) _inst_2 (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u1, max u4 u3, u2} R R S (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (Module.toDistribMulAction.{u1, max u2 u3} S (X -> M) _inst_2 (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (Pi.module.{u3, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9))) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u2 u4) u3, max u2 u3, max (max u2 u4) u3} S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (X -> M) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u2 u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (X -> M) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u1, max u4 u3, u2} R R S (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) 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Case conversion may be inaccurate. Consider using '#align finsupp.llift_symm_apply Finsupp.llift_symm_applyₓ'. -/
@[simp]
theorem llift_symm_apply (f : (X →₀ R) →ₗ[R] M) (x : X) :
@@ -774,10 +726,7 @@ theorem lmapDomain_id : (lmapDomain M R id : (α →₀ M) →ₗ[R] α →₀ M
#align finsupp.lmap_domain_id Finsupp.lmapDomain_id
/- warning: finsupp.lmap_domain_comp -> Finsupp.lmapDomain_comp is a dubious translation:
-lean 3 declaration is
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Case conversion may be inaccurate. Consider using '#align finsupp.lmap_domain_comp Finsupp.lmapDomain_compₓ'. -/
theorem lmapDomain_comp (f : α → α') (g : α' → α'') :
lmapDomain M R (g ∘ f) = (lmapDomain M R g).comp (lmapDomain M R f) :=
@@ -800,10 +749,7 @@ theorem supported_comap_lmapDomain (f : α → α') (s : Set α') :
#align finsupp.supported_comap_lmap_domain Finsupp.supported_comap_lmapDomain
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Case conversion may be inaccurate. Consider using '#align finsupp.lmap_domain_supported Finsupp.lmapDomain_supportedₓ'. -/
theorem lmapDomain_supported [Nonempty α] (f : α → α') (s : Set α) :
(supported M R s).map (lmapDomain M R f) = supported M R (f '' s) :=
@@ -914,10 +860,7 @@ theorem total_apply (l : α →₀ R) : Finsupp.total α M R v l = l.Sum fun i a
#align finsupp.total_apply Finsupp.total_apply
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Case conversion may be inaccurate. Consider using '#align finsupp.total_apply_of_mem_supported Finsupp.total_apply_of_mem_supportedₓ'. -/
theorem total_apply_of_mem_supported {l : α →₀ R} {s : Finset α}
(hs : l ∈ supported R R (↑s : Set α)) : Finsupp.total α M R v l = s.Sum fun i => l i • v i :=
@@ -962,10 +905,7 @@ theorem total_zero : Finsupp.total α M R 0 = 0 :=
variable {α M}
/- warning: finsupp.apply_total -> Finsupp.apply_total is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align finsupp.apply_total Finsupp.apply_totalₓ'. -/
theorem apply_total (f : M →ₗ[R] M') (v) (l : α →₀ R) :
f (Finsupp.total α M R v l) = Finsupp.total α M' R (f ∘ v) l := by
@@ -1044,10 +984,7 @@ theorem range_total : (Finsupp.total α M R v).range = span R (range v) :=
#align finsupp.range_total Finsupp.range_total
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Case conversion may be inaccurate. Consider using '#align finsupp.lmap_domain_total Finsupp.lmapDomain_totalₓ'. -/
theorem lmapDomain_total (f : α → α') (g : M →ₗ[R] M') (h : ∀ i, g (v i) = v' (f i)) :
(Finsupp.total α' M' R v').comp (lmapDomain R R f) = g.comp (Finsupp.total α M R v) := by
@@ -1055,10 +992,7 @@ theorem lmapDomain_total (f : α → α') (g : M →ₗ[R] M') (h : ∀ i, g (v
#align finsupp.lmap_domain_total Finsupp.lmapDomain_total
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Case conversion may be inaccurate. Consider using '#align finsupp.total_comp_lmap_domain Finsupp.total_comp_lmapDomainₓ'. -/
theorem total_comp_lmapDomain (f : α → α') :
(Finsupp.total α' M' R v').comp (Finsupp.lmapDomain R R f) = Finsupp.total α M' R (v' ∘ f) :=
@@ -1068,10 +1002,7 @@ theorem total_comp_lmapDomain (f : α → α') :
#align finsupp.total_comp_lmap_domain Finsupp.total_comp_lmapDomain
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Case conversion may be inaccurate. Consider using '#align finsupp.total_emb_domain Finsupp.total_embDomainₓ'. -/
@[simp]
theorem total_embDomain (f : α ↪ α') (l : α →₀ R) :
@@ -1080,10 +1011,7 @@ theorem total_embDomain (f : α ↪ α') (l : α →₀ R) :
#align finsupp.total_emb_domain Finsupp.total_embDomain
/- warning: finsupp.total_map_domain -> Finsupp.total_mapDomain is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align finsupp.total_map_domain Finsupp.total_mapDomainₓ'. -/
@[simp]
theorem total_mapDomain (f : α → α') (l : α →₀ R) :
@@ -1092,10 +1020,7 @@ theorem total_mapDomain (f : α → α') (l : α →₀ R) :
#align finsupp.total_map_domain Finsupp.total_mapDomain
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Case conversion may be inaccurate. Consider using '#align finsupp.total_equiv_map_domain Finsupp.total_equivMapDomainₓ'. -/
@[simp]
theorem total_equivMapDomain (f : α ≃ α') (l : α →₀ R) :
@@ -1115,10 +1040,7 @@ theorem span_eq_range_total (s : Set M) : span R s = (Finsupp.total s M R coe).r
#align finsupp.span_eq_range_total Finsupp.span_eq_range_total
/- warning: finsupp.mem_span_iff_total -> Finsupp.mem_span_iff_total is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align finsupp.mem_span_iff_total Finsupp.mem_span_iff_totalₓ'. -/
theorem mem_span_iff_total (s : Set M) (x : M) :
x ∈ span R s ↔ ∃ l : s →₀ R, Finsupp.total s M R coe l = x :=
@@ -1141,10 +1063,7 @@ theorem mem_span_range_iff_exists_finsupp {v : α → M} {x : M} :
variable (R)
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Case conversion may be inaccurate. Consider using '#align finsupp.span_image_eq_map_total Finsupp.span_image_eq_map_totalₓ'. -/
theorem span_image_eq_map_total (s : Set α) :
span R (v '' s) = Submodule.map (Finsupp.total α M R v) (supported R R s) :=
@@ -1167,10 +1086,7 @@ theorem span_image_eq_map_total (s : Set α) :
#align finsupp.span_image_eq_map_total Finsupp.span_image_eq_map_total
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Case conversion may be inaccurate. Consider using '#align finsupp.mem_span_image_iff_total Finsupp.mem_span_image_iff_totalₓ'. -/
theorem mem_span_image_iff_total {s : Set α} {x : M} :
x ∈ span R (v '' s) ↔ ∃ l ∈ supported R R s, Finsupp.total α M R v l = x :=
@@ -1180,10 +1096,7 @@ theorem mem_span_image_iff_total {s : Set α} {x : M} :
#align finsupp.mem_span_image_iff_total Finsupp.mem_span_image_iff_total
/- warning: finsupp.total_option -> Finsupp.total_option is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align finsupp.total_option Finsupp.total_optionₓ'. -/
theorem total_option (v : Option α → M) (f : Option α →₀ R) :
Finsupp.total (Option α) M R v f =
@@ -1192,10 +1105,7 @@ theorem total_option (v : Option α → M) (f : Option α →₀ R) :
#align finsupp.total_option Finsupp.total_option
/- warning: finsupp.total_total -> Finsupp.total_total is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align finsupp.total_total Finsupp.total_totalₓ'. -/
theorem total_total {α β : Type _} (A : α → M) (B : β → α →₀ R) (f : β →₀ R) :
Finsupp.total α M R A (Finsupp.total β (α →₀ R) R B f) =
@@ -1225,10 +1135,7 @@ theorem total_fin_zero (f : Fin 0 → M) : Finsupp.total (Fin 0) M R f = 0 :=
variable (α) (M) (v)
/- warning: finsupp.total_on -> Finsupp.totalOn is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align finsupp.total_on Finsupp.totalOnₓ'. -/
/-- `finsupp.total_on M v s` interprets `p : α →₀ R` as a linear combination of a
subset of the vectors in `v`, mapping it to the span of those vectors.
@@ -1243,10 +1150,7 @@ protected def totalOn (s : Set α) : supported R R s →ₗ[R] span R (v '' s) :
variable {α} {M} {v}
/- warning: finsupp.total_on_range -> Finsupp.totalOn_range is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align finsupp.total_on_range Finsupp.totalOn_rangeₓ'. -/
theorem totalOn_range (s : Set α) : (Finsupp.totalOn α M R v s).range = ⊤ :=
by
@@ -1257,10 +1161,7 @@ theorem totalOn_range (s : Set α) : (Finsupp.totalOn α M R v s).range = ⊤ :=
#align finsupp.total_on_range Finsupp.totalOn_range
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Case conversion may be inaccurate. Consider using '#align finsupp.total_comp Finsupp.total_compₓ'. -/
theorem total_comp (f : α' → α) :
Finsupp.total α' M R (v ∘ f) = (Finsupp.total α M R v).comp (lmapDomain R R f) :=
@@ -1270,10 +1171,7 @@ theorem total_comp (f : α' → α) :
#align finsupp.total_comp Finsupp.total_comp
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+<too large>
Case conversion may be inaccurate. Consider using '#align finsupp.total_comap_domain Finsupp.total_comapDomainₓ'. -/
theorem total_comapDomain (f : α → α') (l : α' →₀ R) (hf : Set.InjOn f (f ⁻¹' ↑l.support)) :
Finsupp.total α M R v (Finsupp.comapDomain f l hf) =
@@ -1315,10 +1213,7 @@ protected def domLCongr {α₁ α₂ : Type _} (e : α₁ ≃ α₂) : (α₁
#align finsupp.dom_lcongr Finsupp.domLCongr
/- warning: finsupp.dom_lcongr_apply -> Finsupp.domLCongr_apply is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align finsupp.dom_lcongr_apply Finsupp.domLCongr_applyₓ'. -/
@[simp]
theorem domLCongr_apply {α₁ : Type _} {α₂ : Type _} (e : α₁ ≃ α₂) (v : α₁ →₀ M) :
@@ -1338,10 +1233,7 @@ theorem domLCongr_refl : Finsupp.domLCongr (Equiv.refl α) = LinearEquiv.refl R
#align finsupp.dom_lcongr_refl Finsupp.domLCongr_refl
/- warning: finsupp.dom_lcongr_trans -> Finsupp.domLCongr_trans is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align finsupp.dom_lcongr_trans Finsupp.domLCongr_transₓ'. -/
theorem domLCongr_trans {α₁ α₂ α₃ : Type _} (f : α₁ ≃ α₂) (f₂ : α₂ ≃ α₃) :
(Finsupp.domLCongr f).trans (Finsupp.domLCongr f₂) =
@@ -1362,10 +1254,7 @@ theorem domLCongr_symm {α₁ α₂ : Type _} (f : α₁ ≃ α₂) :
#align finsupp.dom_lcongr_symm Finsupp.domLCongr_symm
/- warning: finsupp.dom_lcongr_single -> Finsupp.domLCongr_single is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align finsupp.dom_lcongr_single Finsupp.domLCongr_singleₓ'. -/
@[simp]
theorem domLCongr_single {α₁ : Type _} {α₂ : Type _} (e : α₁ ≃ α₂) (i : α₁) (m : M) :
@@ -1374,10 +1263,7 @@ theorem domLCongr_single {α₁ : Type _} {α₂ : Type _} (e : α₁ ≃ α₂)
#align finsupp.dom_lcongr_single Finsupp.domLCongr_single
/- warning: finsupp.congr -> Finsupp.congr is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align finsupp.congr Finsupp.congrₓ'. -/
/-- An equivalence of sets induces a linear equivalence of `finsupp`s supported on those sets. -/
noncomputable def congr {α' : Type _} (s : Set α) (t : Set α') (e : s ≃ t) :
@@ -1418,10 +1304,7 @@ theorem mapRange.linearMap_id :
#align finsupp.map_range.linear_map_id Finsupp.mapRange.linearMap_id
/- warning: finsupp.map_range.linear_map_comp -> Finsupp.mapRange.linearMap_comp is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align finsupp.map_range.linear_map_comp Finsupp.mapRange.linearMap_compₓ'. -/
theorem mapRange.linearMap_comp (f : N →ₗ[R] P) (f₂ : M →ₗ[R] N) :
(mapRange.linearMap (f.comp f₂) : (α →₀ _) →ₗ[R] _) =
@@ -1470,10 +1353,7 @@ theorem mapRange.linearEquiv_refl :
#align finsupp.map_range.linear_equiv_refl Finsupp.mapRange.linearEquiv_refl
/- warning: finsupp.map_range.linear_equiv_trans -> Finsupp.mapRange.linearEquiv_trans is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align finsupp.map_range.linear_equiv_trans Finsupp.mapRange.linearEquiv_transₓ'. -/
theorem mapRange.linearEquiv_trans (f : M ≃ₗ[R] N) (f₂ : N ≃ₗ[R] P) :
(mapRange.linearEquiv (f.trans f₂) : (α →₀ _) ≃ₗ[R] _) =
@@ -1530,10 +1410,7 @@ def lcongr {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N) : (ι →
#align finsupp.lcongr Finsupp.lcongr
/- warning: finsupp.lcongr_single -> Finsupp.lcongr_single is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align finsupp.lcongr_single Finsupp.lcongr_singleₓ'. -/
@[simp]
theorem lcongr_single {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N) (i : ι) (m : M) :
@@ -1541,10 +1418,7 @@ theorem lcongr_single {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N)
#align finsupp.lcongr_single Finsupp.lcongr_single
/- warning: finsupp.lcongr_apply_apply -> Finsupp.lcongr_apply_apply is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align finsupp.lcongr_apply_apply Finsupp.lcongr_apply_applyₓ'. -/
@[simp]
theorem lcongr_apply_apply {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N) (f : ι →₀ M) (k : κ) :
@@ -1553,10 +1427,7 @@ theorem lcongr_apply_apply {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[
#align finsupp.lcongr_apply_apply Finsupp.lcongr_apply_apply
/- warning: finsupp.lcongr_symm_single -> Finsupp.lcongr_symm_single is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align finsupp.lcongr_symm_single Finsupp.lcongr_symm_singleₓ'. -/
theorem lcongr_symm_single {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N) (k : κ) (n : N) :
(lcongr e₁ e₂).symm (Finsupp.single k n) = Finsupp.single (e₁.symm k) (e₂.symm n) :=
@@ -1566,10 +1437,7 @@ theorem lcongr_symm_single {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[
#align finsupp.lcongr_symm_single Finsupp.lcongr_symm_single
/- warning: finsupp.lcongr_symm -> Finsupp.lcongr_symm is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align finsupp.lcongr_symm Finsupp.lcongr_symmₓ'. -/
@[simp]
theorem lcongr_symm {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N) :
@@ -1604,10 +1472,7 @@ def sumFinsuppLEquivProdFinsupp {α β : Type _} : (Sum α β →₀ M) ≃ₗ[R
#align finsupp.sum_finsupp_lequiv_prod_finsupp Finsupp.sumFinsuppLEquivProdFinsupp
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+<too large>
Case conversion may be inaccurate. Consider using '#align finsupp.fst_sum_finsupp_lequiv_prod_finsupp Finsupp.fst_sumFinsuppLEquivProdFinsuppₓ'. -/
theorem fst_sumFinsuppLEquivProdFinsupp {α β : Type _} (f : Sum α β →₀ M) (x : α) :
(sumFinsuppLEquivProdFinsupp R f).1 x = f (Sum.inl x) :=
@@ -1615,10 +1480,7 @@ theorem fst_sumFinsuppLEquivProdFinsupp {α β : Type _} (f : Sum α β →₀ M
#align finsupp.fst_sum_finsupp_lequiv_prod_finsupp Finsupp.fst_sumFinsuppLEquivProdFinsupp
/- warning: finsupp.snd_sum_finsupp_lequiv_prod_finsupp -> Finsupp.snd_sumFinsuppLEquivProdFinsupp is a dubious translation:
-lean 3 declaration is
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M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Prod.instAddCommMonoidSum.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} β M _inst_3)))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} R (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M 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_inst_1 _inst_3 _inst_4))) R (Finsupp.{max u3 u4, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (Finsupp.{max u3 u4, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{max u4 u3, u2} (Sum.{u4, u3} α β) M _inst_3)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Prod.instAddCommMonoidSum.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α 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(Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (LinearEquiv.{u1, u1, max u2 u3 u4, max (max u2 u3) u2 u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{max u3 u4, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.addCommMonoid.{max u4 u3, u2} (Sum.{u4, u3} α β) M _inst_3) (Prod.instAddCommMonoidSum.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M 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+<too large>
Case conversion may be inaccurate. Consider using '#align finsupp.snd_sum_finsupp_lequiv_prod_finsupp Finsupp.snd_sumFinsuppLEquivProdFinsuppₓ'. -/
theorem snd_sumFinsuppLEquivProdFinsupp {α β : Type _} (f : Sum α β →₀ M) (y : β) :
(sumFinsuppLEquivProdFinsupp R f).2 y = f (Sum.inr y) :=
@@ -1626,10 +1488,7 @@ theorem snd_sumFinsuppLEquivProdFinsupp {α β : Type _} (f : Sum α β →₀ M
#align finsupp.snd_sum_finsupp_lequiv_prod_finsupp Finsupp.snd_sumFinsuppLEquivProdFinsupp
/- warning: finsupp.sum_finsupp_lequiv_prod_finsupp_symm_inl -> Finsupp.sumFinsuppLEquivProdFinsupp_symm_inl is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align finsupp.sum_finsupp_lequiv_prod_finsupp_symm_inl Finsupp.sumFinsuppLEquivProdFinsupp_symm_inlₓ'. -/
theorem sumFinsuppLEquivProdFinsupp_symm_inl {α β : Type _} (fg : (α →₀ M) × (β →₀ M)) (x : α) :
((sumFinsuppLEquivProdFinsupp R).symm fg) (Sum.inl x) = fg.1 x :=
@@ -1637,10 +1496,7 @@ theorem sumFinsuppLEquivProdFinsupp_symm_inl {α β : Type _} (fg : (α →₀ M
#align finsupp.sum_finsupp_lequiv_prod_finsupp_symm_inl Finsupp.sumFinsuppLEquivProdFinsupp_symm_inl
/- warning: finsupp.sum_finsupp_lequiv_prod_finsupp_symm_inr -> Finsupp.sumFinsuppLEquivProdFinsupp_symm_inr is a dubious translation:
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(Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) => Finsupp.{max u3 u4, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _x) (SMulHomClass.toFunLike.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β 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u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Prod.instAddCommMonoidSum.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} β M _inst_3)))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} R (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Prod.instAddCommMonoidSum.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} β M _inst_3))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} R (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Prod.instAddCommMonoidSum.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M 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(AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (Finsupp.{max u3 u4, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{max u4 u3, u2} (Sum.{u4, u3} α β) M _inst_3)) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} R (Finsupp.{max u3 u4, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{max u4 u3, u2} (Sum.{u4, u3} α β) M _inst_3) (Finsupp.module.{max u4 u3, u2, u1} (Sum.{u4, u3} α β) M R _inst_1 _inst_3 _inst_4))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{max u3 u4, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Prod.instAddCommMonoidSum.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} β M _inst_3)) (Finsupp.addCommMonoid.{max u4 u3, u2} (Sum.{u4, u3} α β) M _inst_3) (Prod.module.{u1, max u2 u4, max u2 u3} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M 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+<too large>
Case conversion may be inaccurate. Consider using '#align finsupp.sum_finsupp_lequiv_prod_finsupp_symm_inr Finsupp.sumFinsuppLEquivProdFinsupp_symm_inrₓ'. -/
theorem sumFinsuppLEquivProdFinsupp_symm_inr {α β : Type _} (fg : (α →₀ M) × (β →₀ M)) (y : β) :
((sumFinsuppLEquivProdFinsupp R).symm fg) (Sum.inr y) = fg.2 y :=
@@ -1674,10 +1530,7 @@ noncomputable def sigmaFinsuppLEquivPiFinsupp {M : Type _} {ιs : η → Type _}
#align finsupp.sigma_finsupp_lequiv_pi_finsupp Finsupp.sigmaFinsuppLEquivPiFinsupp
/- warning: finsupp.sigma_finsupp_lequiv_pi_finsupp_apply -> Finsupp.sigmaFinsuppLEquivPiFinsupp_apply is a dubious translation:
-lean 3 declaration is
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Case conversion may be inaccurate. Consider using '#align finsupp.sigma_finsupp_lequiv_pi_finsupp_apply Finsupp.sigmaFinsuppLEquivPiFinsupp_applyₓ'. -/
@[simp]
theorem sigmaFinsuppLEquivPiFinsupp_apply {M : Type _} {ιs : η → Type _} [AddCommMonoid M]
@@ -1686,10 +1539,7 @@ theorem sigmaFinsuppLEquivPiFinsupp_apply {M : Type _} {ιs : η → Type _} [Ad
#align finsupp.sigma_finsupp_lequiv_pi_finsupp_apply Finsupp.sigmaFinsuppLEquivPiFinsupp_apply
/- warning: finsupp.sigma_finsupp_lequiv_pi_finsupp_symm_apply -> Finsupp.sigmaFinsuppLEquivPiFinsupp_symm_apply is a dubious translation:
-lean 3 declaration is
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Finsupp.addCommMonoid.{u3, u4} (ιs i) M _inst_11)) (Pi.module.{u1, max u4 u3, u2} η (fun (j : η) => Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) R _inst_1 (fun (i : η) => Finsupp.addCommMonoid.{u3, u4} (ιs i) M _inst_11) (fun (i : η) => Finsupp.module.{u3, u4, u2} (ιs i) M R _inst_1 _inst_11 _inst_12)))))) (SMulZeroClass.toSMul.{u2, max (max u3 u4) u1} R (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (AddMonoid.toZero.{max (max u3 u4) u1} (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u1} (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (Finsupp.addCommMonoid.{max u1 u3, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M _inst_11))) (DistribSMul.toSMulZeroClass.{u2, max (max u3 u4) u1} R (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (AddMonoid.toAddZeroClass.{max (max u3 u4) u1} (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u1} (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (Finsupp.addCommMonoid.{max u1 u3, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M _inst_11))) (DistribMulAction.toDistribSMul.{u2, max (max u3 u4) u1} R (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u1} (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (Finsupp.addCommMonoid.{max u1 u3, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M _inst_11)) (Module.toDistribMulAction.{u2, max (max u3 u4) u1} R (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) _inst_1 (Finsupp.addCommMonoid.{max u1 u3, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M _inst_11) (Finsupp.module.{max u1 u3, u4, u2} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M R _inst_1 _inst_11 _inst_12))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u1, u2, max (max u3 u4) u1, max (max u3 u4) u1} (LinearEquiv.{u2, u2, max (max u3 u4) u1, max (max u3 u4) u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) 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_inst_12)) R (forall (j : η), Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u1} (forall (j : η), Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (Pi.addCommMonoid.{u1, max u4 u3} η (fun (j : η) => Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (fun (i : η) => Finsupp.addCommMonoid.{u3, u4} (ιs i) M _inst_11))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u1} (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (Finsupp.addCommMonoid.{max u1 u3, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M _inst_11)) (Module.toDistribMulAction.{u2, max (max u3 u4) u1} R (forall (j : η), Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) _inst_1 (Pi.addCommMonoid.{u1, max u4 u3} η (fun (j : η) => Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (fun (i : η) => Finsupp.addCommMonoid.{u3, u4} (ιs i) M _inst_11)) (Pi.module.{u1, max u4 u3, u2} η (fun (j : η) => Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) R _inst_1 (fun (i : η) => Finsupp.addCommMonoid.{u3, u4} (ιs i) M _inst_11) (fun (i : η) => Finsupp.module.{u3, u4, u2} (ιs i) M R _inst_1 _inst_11 _inst_12))) (Module.toDistribMulAction.{u2, max (max u3 u4) u1} R (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) _inst_1 (Finsupp.addCommMonoid.{max u1 u3, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M _inst_11) (Finsupp.module.{max u1 u3, u4, u2} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M R _inst_1 _inst_11 _inst_12)) (SemilinearMapClass.distribMulActionHomClass.{u2, max (max u3 u4) u1, max (max u3 u4) u1, max (max u3 u4) u1} R (forall (j : η), Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (LinearEquiv.{u2, u2, max (max u3 u4) u1, max (max u3 u4) u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (forall (j : η), Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (Pi.addCommMonoid.{u1, max u4 u3} η (fun (j : η) => Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (fun (i : η) => Finsupp.addCommMonoid.{u3, u4} (ιs i) M _inst_11)) (Finsupp.addCommMonoid.{max u1 u3, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M _inst_11) (Pi.module.{u1, max u4 u3, u2} η (fun (j : η) => Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) R _inst_1 (fun (i : η) => Finsupp.addCommMonoid.{u3, u4} (ιs i) M _inst_11) (fun (i : η) => Finsupp.module.{u3, u4, u2} (ιs i) M R _inst_1 _inst_11 _inst_12)) (Finsupp.module.{max u1 u3, u4, u2} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M R _inst_1 _inst_11 _inst_12)) _inst_1 (Pi.addCommMonoid.{u1, max u4 u3} η (fun (j : η) => Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (fun (i : η) => Finsupp.addCommMonoid.{u3, u4} (ιs i) M _inst_11)) (Finsupp.addCommMonoid.{max u1 u3, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M _inst_11) (Pi.module.{u1, max u4 u3, u2} η (fun (j : η) => Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) R _inst_1 (fun (i : η) => Finsupp.addCommMonoid.{u3, u4} (ιs i) M _inst_11) (fun (i : η) => Finsupp.module.{u3, u4, u2} (ιs i) M R _inst_1 _inst_11 _inst_12)) (Finsupp.module.{max u1 u3, u4, u2} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M R _inst_1 _inst_11 _inst_12) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max (max u3 u4) u1, max (max u3 u4) u1, max (max u3 u4) u1} R R (forall (j : η), Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (LinearEquiv.{u2, u2, max (max u3 u4) u1, max (max u3 u4) u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} 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Case conversion may be inaccurate. Consider using '#align finsupp.sigma_finsupp_lequiv_pi_finsupp_symm_apply Finsupp.sigmaFinsuppLEquivPiFinsupp_symm_applyₓ'. -/
@[simp]
theorem sigmaFinsuppLEquivPiFinsupp_symm_apply {M : Type _} {ιs : η → Type _} [AddCommMonoid M]
@@ -1724,10 +1574,7 @@ noncomputable def finsuppProdLEquiv {α β : Type _} (R : Type _) {M : Type _} [
#align finsupp.finsupp_prod_lequiv Finsupp.finsuppProdLEquiv
/- warning: finsupp.finsupp_prod_lequiv_apply -> Finsupp.finsuppProdLEquiv_apply is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align finsupp.finsupp_prod_lequiv_apply Finsupp.finsuppProdLEquiv_applyₓ'. -/
@[simp]
theorem finsuppProdLEquiv_apply {α β R M : Type _} [Semiring R] [AddCommMonoid M] [Module R M]
@@ -1736,10 +1583,7 @@ theorem finsuppProdLEquiv_apply {α β R M : Type _} [Semiring R] [AddCommMonoid
#align finsupp.finsupp_prod_lequiv_apply Finsupp.finsuppProdLEquiv_apply
/- warning: finsupp.finsupp_prod_lequiv_symm_apply -> Finsupp.finsuppProdLEquiv_symm_apply is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align finsupp.finsupp_prod_lequiv_symm_apply Finsupp.finsuppProdLEquiv_symm_applyₓ'. -/
@[simp]
theorem finsuppProdLEquiv_symm_apply {α β R M : Type _} [Semiring R] [AddCommMonoid M] [Module R M]
@@ -1789,20 +1633,14 @@ protected def Fintype.total : (α → M) →ₗ[S] (α → R) →ₗ[R] M
variable {S}
/- warning: fintype.total_apply -> Fintype.total_apply is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] {S : Type.{u4}} [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (f : α -> R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) => (α -> R) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (coeFn.{max (succ (max u1 u2)) (succ (max (max u1 u3) u2)), max (succ (max u1 u2)) (succ (max (max u1 u3) u2))} (LinearMap.{u4, u4, max u1 u2, max (max u1 u3) u2} S S _inst_5 _inst_5 (RingHom.id.{u4} S 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+<too large>
Case conversion may be inaccurate. Consider using '#align fintype.total_apply Fintype.total_applyₓ'. -/
theorem Fintype.total_apply (f) : Fintype.total R S v f = ∑ i, f i • v i :=
rfl
#align fintype.total_apply Fintype.total_apply
/- warning: fintype.total_apply_single -> Fintype.total_apply_single is a dubious translation:
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(Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (i : α) (r : R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R 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(MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (i : α) (r : R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : α -> R) => M) (Pi.single.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) v) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) (Pi.single.{u3, u2} α (fun (ᾰ : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) r (v i))
+<too large>
Case conversion may be inaccurate. Consider using '#align fintype.total_apply_single Fintype.total_apply_singleₓ'. -/
@[simp]
theorem Fintype.total_apply_single (i : α) (r : R) :
@@ -1815,10 +1653,7 @@ theorem Fintype.total_apply_single (i : α) (r : R) :
variable (S)
/- warning: finsupp.total_eq_fintype_total_apply -> Finsupp.total_eq_fintype_total_apply is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] (S : Type.{u4}) [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (x : α -> R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R 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(Semiring.toNonAssocSemiring.{u3} R _inst_2))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))) M _inst_2 _inst_2 (Finsupp.addCommMonoid.{u1, 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- forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (x : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) => M) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (α -> R) (fun (a : α -> R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : α -> R) => Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) a) (SMulHomClass.toFunLike.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (α -> R) (AddMonoid.toZero.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (α -> R) (AddMonoid.toAddZeroClass.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (α -> R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u3 u2, max u3 u2, max u3 u2} R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) 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(a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (α -> R) (AddMonoid.toAddZeroClass.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (α -> R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u3 u2, max u3 u2, max u3 u2} R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u3 u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2)))))) (LinearEquiv.symm.{u2, u2, max u3 u2, max u3 u2} R R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R 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+<too large>
Case conversion may be inaccurate. Consider using '#align finsupp.total_eq_fintype_total_apply Finsupp.total_eq_fintype_total_applyₓ'. -/
theorem Finsupp.total_eq_fintype_total_apply (x : α → R) :
Finsupp.total α M R v ((Finsupp.linearEquivFunOnFinite R R α).symm x) = Fintype.total R S v x :=
@@ -1831,10 +1666,7 @@ theorem Finsupp.total_eq_fintype_total_apply (x : α → R) :
#align finsupp.total_eq_fintype_total_apply Finsupp.total_eq_fintype_total_apply
/- warning: finsupp.total_eq_fintype_total -> Finsupp.total_eq_fintype_total is a dubious translation:
-lean 3 declaration is
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(Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, 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(Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u4, u3, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)
+<too large>
Case conversion may be inaccurate. Consider using '#align finsupp.total_eq_fintype_total Finsupp.total_eq_fintype_totalₓ'. -/
theorem Finsupp.total_eq_fintype_total :
(Finsupp.total α M R v).comp (Finsupp.linearEquivFunOnFinite R R α).symm.toLinearMap =
@@ -1845,10 +1677,7 @@ theorem Finsupp.total_eq_fintype_total :
variable {S}
/- warning: fintype.range_total -> Fintype.range_total is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] {S : Type.{u4}} [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{succ u2} (Submodule.{u3, u2} R M _inst_2 _inst_3 _inst_4) (LinearMap.range.{u3, u3, max u1 u3, u2, max (max u1 u3) u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : 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(MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{succ u4} (Submodule.{u3, u4} R M _inst_2 _inst_3 _inst_4) (LinearMap.range.{u3, u3, max u2 u3, u4, max (max u2 u4) u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R 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+<too large>
Case conversion may be inaccurate. Consider using '#align fintype.range_total Fintype.range_totalₓ'. -/
@[simp]
theorem Fintype.range_total : (Fintype.total R S v).range = Submodule.span R (Set.range v) := by
@@ -1944,10 +1773,7 @@ protected theorem Submodule.finsupp_sum_mem {ι β : Type _} [Zero β] (S : Subm
#align submodule.finsupp_sum_mem Submodule.finsupp_sum_mem
/- warning: linear_map.map_finsupp_total -> LinearMap.map_finsupp_total is a dubious translation:
-lean 3 declaration is
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Case conversion may be inaccurate. Consider using '#align linear_map.map_finsupp_total LinearMap.map_finsupp_totalₓ'. -/
theorem LinearMap.map_finsupp_total (f : M →ₗ[R] N) {ι : Type _} {g : ι → M} (l : ι →₀ R) :
f (Finsupp.total ι M R g l) = Finsupp.total ι N R (f ∘ g) l := by
@@ -2052,10 +1878,7 @@ def splittingOfFinsuppSurjective (f : M →ₗ[R] α →₀ R) (s : Surjective f
#align linear_map.splitting_of_finsupp_surjective LinearMap.splittingOfFinsuppSurjective
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Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_finsupp_surjective_splits LinearMap.splittingOfFinsuppSurjective_splitsₓ'. -/
theorem splittingOfFinsuppSurjective_splits (f : M →ₗ[R] α →₀ R) (s : Surjective f) :
f.comp (splittingOfFinsuppSurjective f s) = LinearMap.id :=
@@ -2069,10 +1892,7 @@ theorem splittingOfFinsuppSurjective_splits (f : M →ₗ[R] α →₀ R) (s : S
#align linear_map.splitting_of_finsupp_surjective_splits LinearMap.splittingOfFinsuppSurjective_splits
/- warning: linear_map.left_inverse_splitting_of_finsupp_surjective -> LinearMap.leftInverse_splittingOfFinsuppSurjective is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align linear_map.left_inverse_splitting_of_finsupp_surjective LinearMap.leftInverse_splittingOfFinsuppSurjectiveₓ'. -/
theorem leftInverse_splittingOfFinsuppSurjective (f : M →ₗ[R] α →₀ R) (s : Surjective f) :
LeftInverse f (splittingOfFinsuppSurjective f s) := fun g =>
@@ -2080,10 +1900,7 @@ theorem leftInverse_splittingOfFinsuppSurjective (f : M →ₗ[R] α →₀ R) (
#align linear_map.left_inverse_splitting_of_finsupp_surjective LinearMap.leftInverse_splittingOfFinsuppSurjective
/- warning: linear_map.splitting_of_finsupp_surjective_injective -> LinearMap.splittingOfFinsuppSurjective_injective is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_finsupp_surjective_injective LinearMap.splittingOfFinsuppSurjective_injectiveₓ'. -/
theorem splittingOfFinsuppSurjective_injective (f : M →ₗ[R] α →₀ R) (s : Surjective f) :
Injective (splittingOfFinsuppSurjective f s) :=
@@ -2105,10 +1922,7 @@ def splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R) (s
#align linear_map.splitting_of_fun_on_fintype_surjective LinearMap.splittingOfFunOnFintypeSurjective
/- warning: linear_map.splitting_of_fun_on_fintype_surjective_splits -> LinearMap.splittingOfFunOnFintypeSurjective_splits is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective_splits LinearMap.splittingOfFunOnFintypeSurjective_splitsₓ'. -/
theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : f.comp (splittingOfFunOnFintypeSurjective f s) = LinearMap.id :=
@@ -2121,10 +1935,7 @@ theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R]
#align linear_map.splitting_of_fun_on_fintype_surjective_splits LinearMap.splittingOfFunOnFintypeSurjective_splits
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+<too large>
Case conversion may be inaccurate. Consider using '#align linear_map.left_inverse_splitting_of_fun_on_fintype_surjective LinearMap.leftInverse_splittingOfFunOnFintypeSurjectiveₓ'. -/
theorem leftInverse_splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : LeftInverse f (splittingOfFunOnFintypeSurjective f s) := fun g =>
mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b
@@ -91,7 +91,7 @@ def lsingle (a : α) : M →ₗ[R] α →₀ M :=
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} [_inst_1 : Semiring.{u4} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] {{φ : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6}} {{ψ : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6}}, (forall (a : α) (b : M), Eq.{succ u3} N (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (fun (_x : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) => (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) -> N) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) φ (Finsupp.single.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) a b)) (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (fun (_x : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) => (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) -> N) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) ψ (Finsupp.single.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) a b))) -> (Eq.{max (succ (max u1 u2)) (succ u3)} (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) φ ψ)
but is expected to have type
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+ forall {α : Type.{u2}} {M : Type.{u3}} {N : Type.{u1}} {R : Type.{u4}} [_inst_1 : Semiring.{u4} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u4, u3} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : Module.{u4, u1} R N _inst_1 _inst_5] {{φ : LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6}} {{ψ : LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6}}, (forall (a : α) (b : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => N) (Finsupp.single.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) a b)) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u3), succ u1} (LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (fun (_x : Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u2 u3, u1} R R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) φ (Finsupp.single.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) a b)) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u3), succ u1} (LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (fun (_x : Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u2 u3, u1} R R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) ψ (Finsupp.single.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) a b))) -> (Eq.{max (max (succ u2) (succ u3)) (succ u1)} (LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) φ ψ)
Case conversion may be inaccurate. Consider using '#align finsupp.lhom_ext Finsupp.lhom_extₓ'. -/
/-- Two `R`-linear maps from `finsupp X M` which agree on each `single x y` agree everywhere. -/
theorem lhom_ext ⦃φ ψ : (α →₀ M) →ₗ[R] N⦄ (h : ∀ a b, φ (single a b) = ψ (single a b)) : φ = ψ :=
@@ -168,7 +168,7 @@ def lsubtypeDomain : (α →₀ M) →ₗ[R] s →₀ M
lean 3 declaration is
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but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (f : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Finsupp.{u3, u2} (Set.Elem.{u3} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) f) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearMap.{u1, u1, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} (Set.Elem.{u3} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} (Set.Elem.{u3} α s) M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} (Set.Elem.{u3} α s) M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (_x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Finsupp.{u3, u2} (Set.Elem.{u3} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u2, max u3 u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} (Set.Elem.{u3} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} (Set.Elem.{u3} α s) M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} (Set.Elem.{u3} α s) M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lsubtypeDomain.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) f) (Finsupp.subtypeDomain.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (fun (x : α) => Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) x s) f)
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (f : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Finsupp.{u3, u2} (Set.Elem.{u3} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) f) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearMap.{u1, u1, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} (Set.Elem.{u3} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} (Set.Elem.{u3} α s) M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} (Set.Elem.{u3} α s) M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (_x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Finsupp.{u3, u2} (Set.Elem.{u3} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u2, max u3 u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} (Set.Elem.{u3} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} (Set.Elem.{u3} α s) M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} (Set.Elem.{u3} α s) M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lsubtypeDomain.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) f) (Finsupp.subtypeDomain.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (fun (x : α) => Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) x s) f)
Case conversion may be inaccurate. Consider using '#align finsupp.lsubtype_domain_apply Finsupp.lsubtypeDomain_applyₓ'. -/
theorem lsubtypeDomain_apply (f : α →₀ M) :
(lsubtypeDomain s : (α →₀ M) →ₗ[R] s →₀ M) f = subtypeDomain (fun x => x ∈ s) f :=
@@ -181,7 +181,7 @@ end LsubtypeDomain
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (a : α) (b : M), Eq.{max (succ u1) (succ u2)} (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (fun (_x : LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) => M -> (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))))) (LinearMap.hasCoeToFun.{u3, u3, u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lsingle.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a) b) (Finsupp.single.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) a b)
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (a : α) (b : M), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) b) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a) b) (Finsupp.single.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) a b)
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (a : α) (b : M), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) b) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a) b) (Finsupp.single.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) a b)
Case conversion may be inaccurate. Consider using '#align finsupp.lsingle_apply Finsupp.lsingle_applyₓ'. -/
@[simp]
theorem lsingle_apply (a : α) (b : M) : (lsingle a : M →ₗ[R] α →₀ M) b = single a b :=
@@ -192,7 +192,7 @@ theorem lsingle_apply (a : α) (b : M) : (lsingle a : M →ₗ[R] α →₀ M) b
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (a : α) (f : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))), Eq.{succ u2} M (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (LinearMap.{u3, u3, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4) => (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u2, u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lapply.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a) f) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (fun (_x : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) => α -> M) (Finsupp.coeFun.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) f a)
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (a : α) (f : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => M) f) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), succ u2} (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (_x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u2, u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lapply.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a) f) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) α (fun (_x : α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) _x) (Finsupp.funLike.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) f a)
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (a : α) (f : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => M) f) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), succ u2} (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (_x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u2, u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lapply.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a) f) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) α (fun (_x : α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) _x) (Finsupp.funLike.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) f a)
Case conversion may be inaccurate. Consider using '#align finsupp.lapply_apply Finsupp.lapply_applyₓ'. -/
@[simp]
theorem lapply_apply (a : α) (f : α →₀ M) : (lapply a : (α →₀ M) →ₗ[R] M) f = f a :=
@@ -399,7 +399,7 @@ section
lean 3 declaration is
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but is expected to have type
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+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (l : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))), Eq.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Subtype.val.{succ (max u3 u2)} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u3 u2, max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Set.{max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Set.instMembershipSet.{max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) x 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(Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.setLike.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) x (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u2, max u3 u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Subtype.{succ (max u3 u2)} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u3 u2, max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.setLike.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) x (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Submodule.addCommMonoid.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Submodule.module.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.restrictDom.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) l)) (Finsupp.filter.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (fun (_x : α) => Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) _x s) l)
Case conversion may be inaccurate. Consider using '#align finsupp.restrict_dom_apply Finsupp.restrictDom_applyₓ'. -/
@[simp]
theorem restrictDom_apply (s : Set α) (l : α →₀ M) :
@@ -608,7 +608,7 @@ def lsum : (α → M →ₗ[R] N) ≃ₗ[S] (α →₀ M) →ₗ[R] N
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toHasSmul.{u4, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u4, u3} R N (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u5, u3} S N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u5, u3} S N (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)), Eq.{max (max (succ u1) (succ u2)) (succ u3)} ((fun (_x : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) => (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) -> N) (coeFn.{max (succ (max u1 u2 u3)) (succ (max (max u1 u2) u3)), max (succ (max u1 u2 u3)) (succ (max (max u1 u2) u3))} (LinearEquiv.{u5, u5, max u1 u2 u3, max (max u1 u2) u3} S S _inst_2 _inst_2 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2) (α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u1, max u2 u3} α (fun (ᾰ : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.Function.module.{u1, u5, max u2 u3} α S (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.module.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.module.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M 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_inst_10) f)) (fun (d : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) => Finsupp.sum.{u1, u2, u3} α M N (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_5 d (fun (i : α) => coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (_x : LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) => M -> N) (LinearMap.hasCoeToFun.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (f i)))
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u4}} {N : Type.{u3}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u3} R S N (SMulZeroClass.toSMul.{u5, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)), Eq.{max (max (succ u2) (succ u4)) (succ u3)} (forall (a : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) a) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) 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(Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) 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(RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f)) (fun (d : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => Finsupp.sum.{u2, u4, u3} α M ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) d) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) _inst_5 d (fun (i : α) => FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f i)))
+ forall {α : Type.{u2}} {M : Type.{u4}} {N : Type.{u3}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u3} R S N (SMulZeroClass.toSMul.{u5, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)), Eq.{max (max (succ u2) (succ u4)) (succ u3)} (forall (a : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) a) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) f) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (fun (_x : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α 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_inst_2 _inst_9 _inst_10)) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (fun (_x : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _x) (SMulHomClass.toFunLike.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 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u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 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_inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f)) (fun (d : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => Finsupp.sum.{u2, u4, u3} α M ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) d) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) _inst_5 d (fun (i : α) => FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f i)))
Case conversion may be inaccurate. Consider using '#align finsupp.coe_lsum Finsupp.coe_lsumₓ'. -/
@[simp]
theorem coe_lsum (f : α → M →ₗ[R] N) : (lsum S f : (α →₀ M) → N) = fun d => d.Sum fun i => f i :=
@@ -619,7 +619,7 @@ theorem coe_lsum (f : α → M →ₗ[R] N) : (lsum S f : (α →₀ M) → N) =
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toHasSmul.{u4, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u4, u3} R N (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u5, u3} S N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u5, u3} S N (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (l : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))), Eq.{succ u3} N (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (fun (_x : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 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but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u4}} {N : Type.{u3}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u3} R S N (SMulZeroClass.toSMul.{u5, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} S N (AddMonoid.toZero.{u3} N 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_inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) 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(Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M 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(RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2} S S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f) l) (Finsupp.sum.{u2, u4, u3} α M N (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) _inst_5 l (fun (b : α) => FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f b)))
+ forall {α : Type.{u2}} {M : Type.{u4}} {N : Type.{u3}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u3} R S N (SMulZeroClass.toSMul.{u5, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (l : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) l) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), succ u3} ((fun 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(Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) 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(Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M 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_inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f) l) (Finsupp.sum.{u2, u4, u3} α M N (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) _inst_5 l (fun (b : α) => FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f b)))
Case conversion may be inaccurate. Consider using '#align finsupp.lsum_apply Finsupp.lsum_applyₓ'. -/
theorem lsum_apply (f : α → M →ₗ[R] N) (l : α →₀ M) : Finsupp.lsum S f l = l.Sum fun b => f b :=
rfl
@@ -629,7 +629,7 @@ theorem lsum_apply (f : α → M →ₗ[R] N) (l : α →₀ M) : Finsupp.lsum S
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toHasSmul.{u4, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u4, u3} R N (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u5, u3} S N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u5, u3} S N (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (i : α) (m : M), Eq.{succ u3} N (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (fun (_x : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) => (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M 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but is expected to have type
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(AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (fun (_x : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _x) (SMulHomClass.toFunLike.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M 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u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2} S S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f) (Finsupp.single.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) i m)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f i) m)
+ forall {α : Type.{u2}} {M : Type.{u4}} {N : Type.{u3}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u3} R S N (SMulZeroClass.toSMul.{u5, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (i : α) (m : M), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) (Finsupp.single.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) i m)) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), succ u3} 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(AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M 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(fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (fun (_x : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _x) (SMulHomClass.toFunLike.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M 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R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) 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(AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2} S S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f) (Finsupp.single.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) i m)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f i) m)
Case conversion may be inaccurate. Consider using '#align finsupp.lsum_single Finsupp.lsum_singleₓ'. -/
theorem lsum_single (f : α → M →ₗ[R] N) (i : α) (m : M) :
Finsupp.lsum S f (Finsupp.single i m) = f i m :=
@@ -640,7 +640,7 @@ theorem lsum_single (f : α → M →ₗ[R] N) (i : α) (m : M) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toHasSmul.{u4, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u4, u3} R N (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u5, u3} S N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u5, u3} S N (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))] (f : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (x : α), Eq.{max (succ u2) (succ u3)} (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (coeFn.{max (succ (max (max u1 u2) u3)) (succ (max u1 u2 u3)), max (succ (max (max u1 u2) u3)) (succ (max u1 u2 u3))} (LinearEquiv.{u5, u5, max (max u1 u2) u3, max u1 u2 u3} S S _inst_2 _inst_2 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2) (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.addCommMonoid.{u1, max u2 u3} α (fun (ᾰ : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.module.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.Function.module.{u1, u5, max u2 u3} α S (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.module.{u4, u4, u5, u2, u3} R R S M N _inst_1 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u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.addCommMonoid.{u1, max u2 u3} α (fun (ᾰ : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.module.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.Function.module.{u1, u5, max u2 u3} α S (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.module.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10))) => (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) -> α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearEquiv.hasCoeToFun.{u5, u5, max (max u1 u2) u3, max u1 u2 u3} S S (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 _inst_2 (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.addCommMonoid.{u1, max u2 u3} α (fun (ᾰ : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.module.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.Function.module.{u1, u5, max u2 u3} α S (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.module.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2)) (LinearEquiv.symm.{u5, u5, max u1 u2 u3, max (max u1 u2) u3} S S (α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u1, max u2 u3} α (fun (ᾰ : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.Function.module.{u1, u5, max u2 u3} α S (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.module.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.module.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2) (Finsupp.lsum.{u1, u2, u3, u4, u5} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10)) f x) (LinearMap.comp.{u4, u4, u4, u2, max u1 u2, u3} R R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 _inst_4 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomCompTriple.right_ids.{u4, u4} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) f (Finsupp.lsingle.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4 x))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u4}} {N : Type.{u2}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : Module.{u5, u2} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u2} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u2} R S N (SMulZeroClass.toSMul.{u5, u2} R N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u2} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u2} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (Module.toMulActionWithZero.{u5, u2} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u2} S N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u2} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u2} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (Module.toMulActionWithZero.{u1, u2} S N _inst_2 _inst_5 _inst_9))))] (f : LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (x : α), Eq.{max (succ u4) (succ u2)} (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (max (succ u2) (succ u4)) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (fun (_x : LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) => α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _x) (SMulHomClass.toFunLike.{max (max u2 u4) u3, u1, max (max u2 u4) u3, max (max u2 u4) u3} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (SMulZeroClass.toSMul.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (SMulZeroClass.toSMul.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u4) u3, u1, max (max u2 u4) u3, max (max u2 u4) u3} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u2 u4) u3, max (max u2 u4) u3, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3, max (max u2 u4) u3} S S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 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u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) _inst_2 _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun 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_inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (LinearEquiv.symm.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (ᾰ : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (Finsupp.lsum.{u3, u4, u2, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10)) f x) (LinearMap.comp.{u5, u5, u5, u4, max u3 u4, u2} R R R M (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 _inst_4 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHomCompTriple.ids.{u5, u5} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) f (Finsupp.lsingle.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4 x))
+ forall {α : Type.{u3}} {M : Type.{u4}} {N : Type.{u2}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : Module.{u5, u2} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u2} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u2} R S N (SMulZeroClass.toSMul.{u5, u2} R N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u2} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u2} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (Module.toMulActionWithZero.{u5, u2} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u2} S N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u2} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u2} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (Module.toMulActionWithZero.{u1, u2} S N _inst_2 _inst_5 _inst_9))))] (f : LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (x : α), Eq.{max (succ u4) (succ u2)} (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (max (succ u2) (succ u4)) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (fun (_x : LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) => α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _x) (SMulHomClass.toFunLike.{max (max u2 u4) u3, u1, max (max u2 u4) u3, max (max u2 u4) u3} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (SMulZeroClass.toSMul.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (SMulZeroClass.toSMul.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u4) u3, u1, max (max u2 u4) u3, max (max u2 u4) u3} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u2 u4) u3, max (max u2 u4) u3, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3, max (max u2 u4) u3} S S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 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u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) _inst_2 _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun 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_inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M 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_inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (LinearEquiv.symm.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (ᾰ : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 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(RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (Finsupp.lsum.{u3, u4, u2, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10)) f x) (LinearMap.comp.{u5, u5, u5, u4, max u3 u4, u2} R R R M (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 _inst_4 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHomCompTriple.ids.{u5, u5} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) f (Finsupp.lsingle.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4 x))
Case conversion may be inaccurate. Consider using '#align finsupp.lsum_symm_apply Finsupp.lsum_symm_applyₓ'. -/
theorem lsum_symm_apply (f : (α →₀ M) →ₗ[R] N) (x : α) : (lsum S).symm f x = f.comp (lsingle x) :=
rfl
@@ -670,7 +670,7 @@ noncomputable def lift : (X → M) ≃+ ((X →₀ R) →ₗ[R] M) :=
lean 3 declaration is
forall (M : Type.{u1}) (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u3}) (f : LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (x : X), Eq.{succ u1} M (coeFn.{max (succ (max (max u3 u2) u1)) (succ 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(NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.instAdd.{u3, u1} X (fun (ᾰ : X) => M) (fun (i : X) => AddZeroClass.toHasAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (fun (_x : AddEquiv.{max (max u3 u2) u1, max u3 u1} (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R 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but is expected to have type
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Case conversion may be inaccurate. Consider using '#align finsupp.lift_symm_apply Finsupp.lift_symm_applyₓ'. -/
@[simp]
theorem lift_symm_apply (f) (x) : ((lift M R X).symm f) x = f (single x 1) :=
@@ -681,7 +681,7 @@ theorem lift_symm_apply (f) (x) : ((lift M R X).symm f) x = f (single x 1) :=
lean 3 declaration is
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(AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4)))) r (f x)))
but is expected to have type
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(AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4))))) r (f x)))
+ forall (M : Type.{u1}) (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u3}) (f : X -> M) (g : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) g) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : X -> M) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (Finsupp.lift.{u1, u2, u3} M R _inst_1 _inst_3 _inst_4 X) f) g) (Finsupp.sum.{u3, u2, u1} X R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) _inst_3 g (fun (x : X) (r : R) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4))))) r (f x)))
Case conversion may be inaccurate. Consider using '#align finsupp.lift_apply Finsupp.lift_applyₓ'. -/
@[simp]
theorem lift_apply (f) (g) : ((lift M R X) f) g = g.Sum fun x r => r • f x :=
@@ -711,7 +711,7 @@ noncomputable def llift : (X → M) ≃ₗ[S] (X →₀ R) →ₗ[R] M :=
lean 3 declaration is
forall (M : Type.{u1}) (R : Type.{u2}) (S : Type.{u3}) [_inst_1 : Semiring.{u2} R] [_inst_2 : Semiring.{u3} S] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u4}) [_inst_9 : Module.{u3, u1} S M _inst_2 _inst_3] [_inst_10 : SMulCommClass.{u2, u3, u1} R S M (SMulZeroClass.toHasSmul.{u2, u1} R M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u1} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u3, u1} S M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u1} S M (MulZeroClass.toHasZero.{u3} S (MulZeroOneClass.toMulZeroClass.{u3} S (MonoidWithZero.toMulZeroOneClass.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)))) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u1} S M (Semiring.toMonoidWithZero.{u3} S _inst_2) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Module.toMulActionWithZero.{u3, u1} S M _inst_2 _inst_3 _inst_9))))] (f : X -> M) (x : Finsupp.{u4, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))), Eq.{succ u1} M 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_inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4)) (AddEquiv.hasCoeToFun.{max u4 u1, max (max u4 u2) u1} (X -> M) (LinearMap.{u2, u2, max u4 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u4, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u4, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u4, u1} X (fun (ᾰ : X) => M) (fun (i : X) => AddZeroClass.toHasAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.hasAdd.{u2, u2, max u4 u2, u1} R R (Finsupp.{u4, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.lift.{u1, u2, u4} M R _inst_1 _inst_3 _inst_4 X) f) x)
but is expected to have type
- forall (M : Type.{u2}) (R : Type.{u3}) (S : Type.{u1}) [_inst_1 : Semiring.{u3} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (X : Type.{u4}) [_inst_9 : Module.{u1, u2} S M _inst_2 _inst_3] [_inst_10 : SMulCommClass.{u3, u1, u2} R S M (SMulZeroClass.toSMul.{u3, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u2} R M (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} S M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} S M (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u1, u2} S M _inst_2 _inst_3 _inst_9))))] (f : X -> M) (x : Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) => M) x) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : X -> M) => LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) f) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (fun (_x : Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u2) (succ u4), max (max (succ u2) (succ u3)) (succ u4)} (LinearEquiv.{u1, u1, max u2 u4, max u2 u3 u4} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R 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_inst_2)) (AddCommMonoid.toAddMonoid.{max u2 u4} (X -> M) (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3))) (Module.toDistribMulAction.{u1, max u2 u4} S (X -> M) _inst_2 (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (Pi.module.{u4, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9)))))) (SMulZeroClass.toSMul.{u1, max (max u2 u3) u4} S (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddMonoid.toZero.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u3) u4} S (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddMonoid.toAddZeroClass.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u3) u4} S (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u2 u3) u4} S (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) _inst_2 (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u3 u4, u2} R R S (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u3) u4, u1, max u2 u4, max (max u2 u3) u4} (LinearEquiv.{u1, u1, max u2 u4, max u2 u3 u4} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u4, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u3 u4, u2} R R S (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max u2 u4} (X -> M) (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Module.toDistribMulAction.{u1, max u2 u4} S (X -> M) _inst_2 (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (Pi.module.{u4, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9))) (Module.toDistribMulAction.{u1, max (max u2 u3) u4} S (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) _inst_2 (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R 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(a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5047 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (LinearMap.instAddLinearMap.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (AddEquiv.instAddEquivClassAddEquiv.{max u2 u4, max (max u2 u3) u4} (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R 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(Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) (Finsupp.lift.{u2, u3, u4} M R _inst_1 _inst_3 _inst_4 X) f) x)
+ forall (M : Type.{u2}) (R : Type.{u3}) (S : Type.{u1}) [_inst_1 : Semiring.{u3} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (X : Type.{u4}) [_inst_9 : Module.{u1, u2} S M _inst_2 _inst_3] [_inst_10 : SMulCommClass.{u3, u1, u2} R S M (SMulZeroClass.toSMul.{u3, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u2} R M (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} S M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} S M (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u1, u2} S M _inst_2 _inst_3 _inst_9))))] (f : X -> M) (x : Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) => M) x) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : X -> M) => LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) f) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (fun (_x : Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u2) (succ u4), max (max (succ u2) (succ u3)) (succ u4)} (LinearEquiv.{u1, u1, max u2 u4, max u2 u3 u4} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_2 _inst_9 _inst_10)) (X -> M) (fun (_x : X -> M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : X -> M) => LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) _x) 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_inst_2)) (AddCommMonoid.toAddMonoid.{max u2 u4} (X -> M) (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3))) (Module.toDistribMulAction.{u1, max u2 u4} S (X -> M) _inst_2 (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (Pi.module.{u4, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9)))))) (SMulZeroClass.toSMul.{u1, max (max u2 u3) u4} S (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddMonoid.toZero.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u3) u4} S (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddMonoid.toAddZeroClass.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u3) u4} S (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u2 u3) u4} S (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) _inst_2 (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u3 u4, u2} R R S (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u3) u4, u1, max u2 u4, max (max u2 u3) u4} (LinearEquiv.{u1, u1, max u2 u4, max u2 u3 u4} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u4, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u3 u4, u2} R R S (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max u2 u4} (X -> M) (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Module.toDistribMulAction.{u1, max u2 u4} S (X -> M) _inst_2 (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (Pi.module.{u4, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9))) (Module.toDistribMulAction.{u1, max (max u2 u3) u4} S (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) _inst_2 (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u3 u4, u2} R R S (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max u2 u4, max (max u2 u3) u4, max (max u2 u3) u4} S (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearEquiv.{u1, u1, max u2 u4, max u2 u3 u4} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (X -> M) (LinearMap.{u3, u3, max u3 u4, 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(Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) (Finsupp.lift.{u2, u3, u4} M R _inst_1 _inst_3 _inst_4 X) f) x)
Case conversion may be inaccurate. Consider using '#align finsupp.llift_apply Finsupp.llift_applyₓ'. -/
@[simp]
theorem llift_apply (f : X → M) (x : X →₀ R) : llift M R S X f x = lift M R X f x :=
@@ -722,7 +722,7 @@ theorem llift_apply (f : X → M) (x : X →₀ R) : llift M R S X f x = lift M
lean 3 declaration is
forall (M : Type.{u1}) (R : Type.{u2}) (S : Type.{u3}) [_inst_1 : Semiring.{u2} R] [_inst_2 : Semiring.{u3} S] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u4}) [_inst_9 : Module.{u3, u1} S M _inst_2 _inst_3] [_inst_10 : SMulCommClass.{u2, u3, u1} R S M (SMulZeroClass.toHasSmul.{u2, u1} R M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u1} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u3, u1} S M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u1} S M (MulZeroClass.toHasZero.{u3} S (MulZeroOneClass.toMulZeroClass.{u3} S (MonoidWithZero.toMulZeroOneClass.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)))) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u1} S M (Semiring.toMonoidWithZero.{u3} S _inst_2) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Module.toMulActionWithZero.{u3, u1} S M _inst_2 _inst_3 _inst_9))))] (f : LinearMap.{u2, u2, max u4 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u4, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u4, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (x : X), Eq.{succ u1} M (coeFn.{max (succ (max (max u4 u2) u1)) (succ (max u4 u1)), max (succ (max (max u4 u2) u1)) (succ (max u4 u1))} (LinearEquiv.{u3, u3, max (max u4 u2) u1, max u4 u1} S S _inst_2 _inst_2 (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2)) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2)) (RingHomInvPair.ids.{u3} S _inst_2) (RingHomInvPair.ids.{u3} S _inst_2) (LinearMap.{u2, u2, max u4 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u4, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u4, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (X -> M) (LinearMap.addCommMonoid.{u2, u2, max u4 u2, u1} R R (Finsupp.{u4, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 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but is expected to have type
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(Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) _inst_2 (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u1, max u4 u3, u2} R R S (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (SMulZeroClass.toSMul.{u1, max u2 u3} S (X -> M) (AddMonoid.toZero.{max u2 u3} (X -> M) (AddCommMonoid.toAddMonoid.{max u2 u3} (X -> M) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)))) (DistribSMul.toSMulZeroClass.{u1, max u2 u3} S (X -> M) (AddMonoid.toAddZeroClass.{max u2 u3} (X -> M) (AddCommMonoid.toAddMonoid.{max u2 u3} (X -> M) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)))) (DistribMulAction.toDistribSMul.{u1, max u2 u3} S (X -> M) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max u2 u3} (X -> M) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3))) (Module.toDistribMulAction.{u1, max u2 u3} S (X -> M) _inst_2 (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (Pi.module.{u3, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u4) u3, u1, max (max u2 u4) u3, max u2 u3} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u2 u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (X -> M) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u1, max u4 u3, u2} R R S (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9))) S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (X -> M) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u3} (X -> M) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) _inst_2 (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u1, max u4 u3, u2} R R S (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (Module.toDistribMulAction.{u1, max u2 u3} S (X -> M) _inst_2 (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (Pi.module.{u3, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9))) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u2 u4) u3, max u2 u3, max (max u2 u4) u3} S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (X -> M) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u2 u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (X -> M) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u1, max u4 u3, u2} R R S (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9))) _inst_2 (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u1, 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(Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u2 u4) u3, max u2 u3} S S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (X -> M) _inst_2 _inst_2 (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u1, max u4 u3, u2} R R S (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R 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u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} X (fun (ᾰ : X) => M) (fun (i : X) => _inst_3)) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.module.{u3, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9)) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u1, max u4 u3, u2} R R S (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (Finsupp.llift.{u2, u4, u1, u3} M R S _inst_1 _inst_2 _inst_3 _inst_4 X _inst_9 _inst_10)) f x) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) (fun (_x : Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) f (Finsupp.single.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)) x (OfNat.ofNat.{u4} R 1 (One.toOfNat1.{u4} R (Semiring.toOne.{u4} R _inst_1)))))
+ forall (M : Type.{u2}) (R : Type.{u4}) (S : Type.{u1}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] (X : Type.{u3}) [_inst_9 : Module.{u1, u2} S M _inst_2 _inst_3] [_inst_10 : SMulCommClass.{u4, u1, u2} R S M (SMulZeroClass.toSMul.{u4, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u4, u2} R M (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u4, u2} R M (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u4, u2} R M _inst_1 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} S M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} S M (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u1, u2} S M _inst_2 _inst_3 _inst_9))))] (f : LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (x : X), Eq.{succ u2} M (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u3)} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u2 u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (X -> M) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u1, max u4 u3, u2} R R S (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9))) (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) => X -> M) _x) (SMulHomClass.toFunLike.{max (max u2 u4) u3, u1, max (max u2 u4) u3, max u2 u3} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u2 u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (X -> M) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u1, max u4 u3, u2} R R S (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9))) S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (X -> M) (SMulZeroClass.toSMul.{u1, max (max u2 u4) u3} S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (AddMonoid.toZero.{max (max u2 u4) u3} (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u4) u3} S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (AddMonoid.toAddZeroClass.{max (max u2 u4) u3} (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u4) u3} S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) _inst_2 (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u1, max u4 u3, u2} R R S (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (SMulZeroClass.toSMul.{u1, max u2 u3} S (X -> M) (AddMonoid.toZero.{max u2 u3} (X -> M) (AddCommMonoid.toAddMonoid.{max u2 u3} (X -> M) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)))) (DistribSMul.toSMulZeroClass.{u1, max u2 u3} S (X -> M) (AddMonoid.toAddZeroClass.{max u2 u3} (X -> M) (AddCommMonoid.toAddMonoid.{max u2 u3} (X -> M) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)))) (DistribMulAction.toDistribSMul.{u1, max u2 u3} S (X -> M) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max u2 u3} (X -> M) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3))) (Module.toDistribMulAction.{u1, max u2 u3} S (X -> M) _inst_2 (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (Pi.module.{u3, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u4) u3, u1, max (max u2 u4) u3, max u2 u3} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u2 u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (X -> M) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u1, max u4 u3, u2} R R S (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9))) S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (X -> M) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u3} (X -> M) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) _inst_2 (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u1, max u4 u3, u2} R R S (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (Module.toDistribMulAction.{u1, max u2 u3} S (X -> M) _inst_2 (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (Pi.module.{u3, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9))) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u2 u4) u3, max u2 u3, max (max u2 u4) u3} S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (X -> M) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u2 u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (X -> M) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) f (Finsupp.single.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)) x (OfNat.ofNat.{u4} R 1 (One.toOfNat1.{u4} R (Semiring.toOne.{u4} R _inst_1)))))
Case conversion may be inaccurate. Consider using '#align finsupp.llift_symm_apply Finsupp.llift_symm_applyₓ'. -/
@[simp]
theorem llift_symm_apply (f : (X →₀ R) →ₗ[R] M) (x : X) :
@@ -754,7 +754,7 @@ def lmapDomain (f : α → α') : (α →₀ M) →ₗ[R] α' →₀ M
lean 3 declaration is
forall {α : Type.{u1}} (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {α' : Type.{u4}} (f : α -> α') (l : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))), Eq.{max (succ u4) (succ u2)} (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (coeFn.{max (succ (max u1 u2)) (succ (max u4 u2)), max (succ (max u1 u2)) (succ (max u4 u2))} (LinearMap.{u3, u3, max u1 u2, max u4 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4)) (fun (_x : LinearMap.{u3, u3, max u1 u2, max u4 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4)) => (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) -> (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))))) (LinearMap.hasCoeToFun.{u3, u3, max u1 u2, max u4 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lmapDomain.{u1, u2, u3, u4} α M R _inst_1 _inst_3 _inst_4 α' f) l) (Finsupp.mapDomain.{u1, u4, u2} α α' M _inst_3 f l)
but is expected to have type
- forall {α : Type.{u4}} (M : Type.{u3}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u1, u3} R M _inst_1 _inst_3] {α' : Type.{u2}} (f : α -> α') (l : Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) l) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u3), max (succ u3) (succ u2)} (LinearMap.{u1, u1, max u3 u4, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.addCommMonoid.{u4, u3} α M _inst_3) (Finsupp.addCommMonoid.{u2, u3} α' M _inst_3) (Finsupp.module.{u4, u3, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u2, u3, u1} α' M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (fun (_x : Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max u3 u2} R R (Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} α M _inst_3) (Finsupp.addCommMonoid.{u2, u3} α' M _inst_3) (Finsupp.module.{u4, u3, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u2, u3, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lmapDomain.{u4, u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 α' f) l) (Finsupp.mapDomain.{u4, u2, u3} α α' M _inst_3 f l)
+ forall {α : Type.{u4}} (M : Type.{u3}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u1, u3} R M _inst_1 _inst_3] {α' : Type.{u2}} (f : α -> α') (l : Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) l) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u3), max (succ u3) (succ u2)} (LinearMap.{u1, u1, max u3 u4, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.addCommMonoid.{u4, u3} α M _inst_3) (Finsupp.addCommMonoid.{u2, u3} α' M _inst_3) (Finsupp.module.{u4, u3, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u2, u3, u1} α' M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (fun (_x : Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max u3 u2} R R (Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} α M _inst_3) (Finsupp.addCommMonoid.{u2, u3} α' M _inst_3) (Finsupp.module.{u4, u3, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u2, u3, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lmapDomain.{u4, u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 α' f) l) (Finsupp.mapDomain.{u4, u2, u3} α α' M _inst_3 f l)
Case conversion may be inaccurate. Consider using '#align finsupp.lmap_domain_apply Finsupp.lmapDomain_applyₓ'. -/
@[simp]
theorem lmapDomain_apply (f : α → α') (l : α →₀ M) :
@@ -907,7 +907,7 @@ variable {α M v}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {v : α -> M} (l : Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v) l) (Finsupp.sum.{u1, u3, u2} α R M (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 l (fun (i : α) (a : R) => SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) a (v i)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {v : α -> M} (l : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 v) l) (Finsupp.sum.{u3, u2, u1} α R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) _inst_3 l (fun (i : α) (a : R) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4))))) a (v i)))
+ forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {v : α -> M} (l : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 v) l) (Finsupp.sum.{u3, u2, u1} α R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) _inst_3 l (fun (i : α) (a : R) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4))))) a (v i)))
Case conversion may be inaccurate. Consider using '#align finsupp.total_apply Finsupp.total_applyₓ'. -/
theorem total_apply (l : α →₀ R) : Finsupp.total α M R v l = l.Sum fun i a => a • v i :=
rfl
@@ -917,7 +917,7 @@ theorem total_apply (l : α →₀ R) : Finsupp.total α M R v l = l.Sum fun i a
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {v : α -> M} {l : Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))} {s : Finset.{u1} α}, (Membership.Mem.{max u1 u3, max u1 u3} (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (SetLike.hasMem.{max u1 u3, max u1 u3} (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) (Submodule.setLike.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)))) l (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} α) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (Finset.Set.hasCoeT.{u1} α))) s))) -> (Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v) l) (Finset.sum.{u2, u1} M α _inst_3 s (fun (i : α) => SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (fun (_x : Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) => α -> R) (Finsupp.coeFun.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) l i) (v i))))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {v : α -> M} {l : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))} {s : Finset.{u3} α}, (Membership.mem.{max u3 u2, max u2 u3} (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 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(Semiring.toModule.{u2} R _inst_1) (Finset.toSet.{u3} α s))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 v) l) (Finset.sum.{u1, u3} M α _inst_3 s (fun (i : α) => HSMul.hSMul.{u2, u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M M (instHSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (SMulZeroClass.toSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M _inst_1 _inst_3 _inst_4))))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) α (fun (_x : α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) _x) (Finsupp.funLike.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) l i) (v i))))
+ forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {v : α -> M} {l : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))} {s : Finset.{u3} α}, (Membership.mem.{max u3 u2, max u2 u3} (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (Submodule.setLike.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)))) l (Finsupp.supported.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1) (Finset.toSet.{u3} α s))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 v) l) (Finset.sum.{u1, u3} M α _inst_3 s (fun (i : α) => HSMul.hSMul.{u2, u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M M (instHSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (SMulZeroClass.toSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M _inst_1 _inst_3 _inst_4))))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) α (fun (_x : α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) _x) (Finsupp.funLike.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) l i) (v i))))
Case conversion may be inaccurate. Consider using '#align finsupp.total_apply_of_mem_supported Finsupp.total_apply_of_mem_supportedₓ'. -/
theorem total_apply_of_mem_supported {l : α →₀ R} {s : Finset α}
(hs : l ∈ supported R R (↑s : Set α)) : Finsupp.total α M R v l = s.Sum fun i => l i • v i :=
@@ -929,7 +929,7 @@ theorem total_apply_of_mem_supported {l : α →₀ R} {s : Finset α}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {v : α -> M} (c : R) (a : α), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v) (Finsupp.single.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) a c)) (SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) c (v a))
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u3}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u1, u3} R M _inst_1 _inst_3] {v : α -> M} (c : R) (a : α), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) (Finsupp.single.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) a c)) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u1), succ u3} (LinearMap.{u1, u1, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u3} R R (Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4 v) (Finsupp.single.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) a c)) (HSMul.hSMul.{u1, u3, u3} R M M (instHSMul.{u1, u3} R M (SMulZeroClass.toSMul.{u1, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u1, u3} R M _inst_1 _inst_3 _inst_4))))) c (v a))
+ forall {α : Type.{u2}} {M : Type.{u3}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u1, u3} R M _inst_1 _inst_3] {v : α -> M} (c : R) (a : α), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) (Finsupp.single.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) a c)) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u1), succ u3} (LinearMap.{u1, u1, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u3} R R (Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4 v) (Finsupp.single.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) a c)) (HSMul.hSMul.{u1, u3, u3} R M M (instHSMul.{u1, u3} R M (SMulZeroClass.toSMul.{u1, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u1, u3} R M _inst_1 _inst_3 _inst_4))))) c (v a))
Case conversion may be inaccurate. Consider using '#align finsupp.total_single Finsupp.total_singleₓ'. -/
@[simp]
theorem total_single (c : R) (a : α) : Finsupp.total α M R v (single a c) = c • v a := by
@@ -940,7 +940,7 @@ theorem total_single (c : R) (a : α) : Finsupp.total α M R v (single a c) = c
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (x : Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u1 u2} (α -> M) 0 (OfNat.mk.{max u1 u2} (α -> M) 0 (Zero.zero.{max u1 u2} (α -> M) (Pi.instZero.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))))))) x) (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))))))
but is expected to have type
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+ forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u3 u1} (α -> M) 0 (Zero.toOfNat0.{max u3 u1} (α -> M) (Pi.instZero.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.6886 : α) => M) (fun (i : α) => AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) _inst_3))))
Case conversion may be inaccurate. Consider using '#align finsupp.total_zero_apply Finsupp.total_zero_applyₓ'. -/
theorem total_zero_apply (x : α →₀ R) : (Finsupp.total α M R 0) x = 0 := by
simp [Finsupp.total_apply]
@@ -965,7 +965,7 @@ variable {α M}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {M' : Type.{u4}} [_inst_9 : AddCommMonoid.{u4} M'] [_inst_10 : Module.{u3, u4} R M' _inst_1 _inst_9] (f : LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_3 _inst_9 _inst_4 _inst_10) (v : α -> M) (l : Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))), Eq.{succ u4} M' (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_3 _inst_9 _inst_4 _inst_10) (fun (_x : LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' 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(x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, u2} R R M _inst_1 _inst_3 _inst_3 M' _inst_4 _inst_10 _inst_9 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_3))) f) v)) l)
Case conversion may be inaccurate. Consider using '#align finsupp.apply_total Finsupp.apply_totalₓ'. -/
theorem apply_total (f : M →ₗ[R] M') (v) (l : α →₀ R) :
f (Finsupp.total α M R v l) = Finsupp.total α M' R (f ∘ v) l := by
@@ -976,7 +976,7 @@ theorem apply_total (f : M →ₗ[R] M') (v) (l : α →₀ R) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] [_inst_11 : Unique.{succ u1} α] (l : Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (v : α -> M), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v) l) (SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (fun (_x : Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) => α -> R) (Finsupp.coeFun.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) l (Inhabited.default.{succ u1} α (Unique.inhabited.{succ u1} α _inst_11))) (v (Inhabited.default.{succ u1} α (Unique.inhabited.{succ u1} α _inst_11))))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] [_inst_11 : Unique.{succ u3} α] (l : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (v : α -> M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 v) l) (HSMul.hSMul.{u2, u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M M (instHSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M (SMulZeroClass.toSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M _inst_1 _inst_3 _inst_4))))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) α (fun (_x : α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) _x) (Finsupp.funLike.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) l (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) (v (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))))
+ forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] [_inst_11 : Unique.{succ u3} α] (l : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (v : α -> M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 v) l) (HSMul.hSMul.{u2, u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M M (instHSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M (SMulZeroClass.toSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M _inst_1 _inst_3 _inst_4))))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) α (fun (_x : α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) _x) (Finsupp.funLike.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) l (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) (v (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))))
Case conversion may be inaccurate. Consider using '#align finsupp.total_unique Finsupp.total_uniqueₓ'. -/
theorem total_unique [Unique α] (l : α →₀ R) (v) :
Finsupp.total α M R v l = l default • v default := by rw [← total_single, ← unique_single l]
@@ -986,7 +986,7 @@ theorem total_unique [Unique α] (l : α →₀ R) (v) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {v : α -> M}, (Function.Surjective.{succ u1, succ u2} α M v) -> (Function.Surjective.{max (succ u1) (succ u3), succ u2} (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {v : α -> M}, (Function.Surjective.{succ u3, succ u2} α M v) -> (Function.Surjective.{max (succ u3) (succ u1), succ u2} (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u1), succ u2} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 v)))
+ forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {v : α -> M}, (Function.Surjective.{succ u3, succ u2} α M v) -> (Function.Surjective.{max (succ u3) (succ u1), succ u2} (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u1), succ u2} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 v)))
Case conversion may be inaccurate. Consider using '#align finsupp.total_surjective Finsupp.total_surjectiveₓ'. -/
theorem total_surjective (h : Function.Surjective v) :
Function.Surjective (Finsupp.total α M R v) :=
@@ -1010,7 +1010,7 @@ theorem total_range (h : Function.Surjective v) : (Finsupp.total α M R v).range
lean 3 declaration is
forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] (M : Type.{u2}) [_inst_11 : AddCommMonoid.{u2} M] [_inst_12 : Module.{u1, u2} R M _inst_1 _inst_11], Function.Surjective.{max (succ u2) (succ u1), succ u2} (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (coeFn.{max (succ (max u2 u1)) (succ u2), max (succ (max u2 u1)) (succ u2)} (LinearMap.{u1, u1, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_11 (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_12) (fun (_x : LinearMap.{u1, u1, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_11 (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_12) => (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u2} R R (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_11 (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_12 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} M M R _inst_1 _inst_11 _inst_12 (id.{succ u2} M)))
but is expected to have type
- forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] (M : Type.{u2}) [_inst_11 : AddCommMonoid.{u2} M] [_inst_12 : Module.{u1, u2} R M _inst_1 _inst_11], Function.Surjective.{max (succ u1) (succ u2), succ u2} (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_11 (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_12) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u2} R R (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_11 (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_12 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} M M R _inst_1 _inst_11 _inst_12 (id.{succ u2} M)))
+ forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] (M : Type.{u2}) [_inst_11 : AddCommMonoid.{u2} M] [_inst_12 : Module.{u1, u2} R M _inst_1 _inst_11], Function.Surjective.{max (succ u1) (succ u2), succ u2} (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_11 (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_12) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u2} R R (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_11 (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_12 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} M M R _inst_1 _inst_11 _inst_12 (id.{succ u2} M)))
Case conversion may be inaccurate. Consider using '#align finsupp.total_id_surjective Finsupp.total_id_surjectiveₓ'. -/
/-- Any module is a quotient of a free module. This is stated as surjectivity of
`finsupp.total M M R id : (M →₀ R) →ₗ[R] M`. -/
@@ -1047,7 +1047,7 @@ theorem range_total : (Finsupp.total α M R v).range = span R (range v) :=
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {α' : Type.{u4}} {M' : Type.{u5}} [_inst_9 : AddCommMonoid.{u5} M'] [_inst_10 : Module.{u3, u5} R M' _inst_1 _inst_9] {v : α -> M} {v' : α' -> M'} (f : α -> α') (g : LinearMap.{u3, u3, u2, u5} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_3 _inst_9 _inst_4 _inst_10), (forall (i : α), Eq.{succ u5} M' (coeFn.{max (succ u2) (succ u5), max (succ u2) (succ u5)} (LinearMap.{u3, u3, u2, u5} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_3 _inst_9 _inst_4 _inst_10) (fun (_x : LinearMap.{u3, u3, u2, u5} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_3 _inst_9 _inst_4 _inst_10) => M -> M') (LinearMap.hasCoeToFun.{u3, u3, u2, u5} R R M M' _inst_1 _inst_1 _inst_3 _inst_9 _inst_4 _inst_10 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) g (v i)) (v' (f i))) -> (Eq.{max (succ (max u1 u3)) (succ u5)} (LinearMap.{u3, u3, max u1 u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) M' (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_10) (LinearMap.comp.{u3, u3, u3, max u1 u3, max u4 u3, u5} R R R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) (Finsupp.{u4, u3} α' R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M' _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.addCommMonoid.{u4, u3} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Finsupp.module.{u4, u3, u3} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_10 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomCompTriple.right_ids.{u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u4, u5, u3} α' M' R _inst_1 _inst_9 _inst_10 v') (Finsupp.lmapDomain.{u1, u3, u3, u4} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) α' f)) (LinearMap.comp.{u3, u3, u3, max u1 u3, u2, u5} R R R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) M M' _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 _inst_9 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 _inst_10 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomCompTriple.right_ids.{u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) g (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v)))
but is expected to have type
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+ forall {α : Type.{u2}} {M : Type.{u4}} (R : Type.{u5}) {_inst_1 : Type.{u1}} {_inst_3 : Type.{u3}} [_inst_4 : Semiring.{u5} R] [α' : AddCommMonoid.{u3} _inst_3] [M' : AddCommMonoid.{u4} M] [_inst_9 : Module.{u5, u3} R _inst_3 _inst_4 α'] [_inst_10 : Module.{u5, u4} R M _inst_4 M'] {v : α -> M} {v' : _inst_1 -> _inst_3} (f : α -> _inst_1) (g : LinearMap.{u5, u5, u4, u3} R R _inst_4 _inst_4 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) M _inst_3 M' α' _inst_10 _inst_9), (forall (i : α), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => _inst_3) (v i)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_4 _inst_4 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) M _inst_3 M' α' _inst_10 _inst_9) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M _inst_3 _inst_4 _inst_4 M' α' _inst_10 _inst_9 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) g (v i)) (v' (f i))) -> (Eq.{max (max (succ u2) (succ u5)) (succ u3)} (LinearMap.{u5, u5, max u5 u2, u3} R R _inst_4 _inst_4 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (Finsupp.{u2, u5} α R (AddMonoid.toZero.{u5} R (AddCommMonoid.toAddMonoid.{u5} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))))) _inst_3 (Finsupp.addCommMonoid.{u2, u5} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))) α' (Finsupp.module.{u2, u5, u5} α R R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Semiring.toModule.{u5} R _inst_4)) _inst_9) (LinearMap.comp.{u5, u5, u5, max u5 u2, max u5 u1, u3} R R R (Finsupp.{u2, u5} α R (AddMonoid.toZero.{u5} R (AddCommMonoid.toAddMonoid.{u5} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))))) (Finsupp.{u1, u5} _inst_1 R (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_4))) _inst_3 _inst_4 _inst_4 _inst_4 (Finsupp.addCommMonoid.{u2, u5} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))) (Finsupp.addCommMonoid.{u1, u5} _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))) α' (Finsupp.module.{u2, u5, u5} α R R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Semiring.toModule.{u5} R _inst_4)) (Finsupp.module.{u1, u5, u5} _inst_1 R R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Semiring.toModule.{u5} R _inst_4)) _inst_9 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHomCompTriple.ids.{u5, u5} R R _inst_4 _inst_4 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Finsupp.total.{u1, u3, u5} _inst_1 _inst_3 R _inst_4 α' _inst_9 v') (Finsupp.lmapDomain.{u2, u5, u5, u1} α R R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Semiring.toModule.{u5} R _inst_4) _inst_1 f)) (LinearMap.comp.{u5, u5, u5, max u2 u5, u4, u3} R R R (Finsupp.{u2, u5} α R (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_4))) M _inst_3 _inst_4 _inst_4 _inst_4 (Finsupp.addCommMonoid.{u2, u5} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))) M' α' (Finsupp.module.{u2, u5, u5} α R R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Semiring.toModule.{u5} R _inst_4)) _inst_10 _inst_9 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHomCompTriple.ids.{u5, u5} R R _inst_4 _inst_4 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) g (Finsupp.total.{u2, u4, u5} α M R _inst_4 M' _inst_10 v)))
Case conversion may be inaccurate. Consider using '#align finsupp.lmap_domain_total Finsupp.lmapDomain_totalₓ'. -/
theorem lmapDomain_total (f : α → α') (g : M →ₗ[R] M') (h : ∀ i, g (v i) = v' (f i)) :
(Finsupp.total α' M' R v').comp (lmapDomain R R f) = g.comp (Finsupp.total α M R v) := by
@@ -1071,7 +1071,7 @@ theorem total_comp_lmapDomain (f : α → α') :
lean 3 declaration is
forall {α : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] {α' : Type.{u3}} {M' : Type.{u4}} [_inst_9 : AddCommMonoid.{u4} M'] [_inst_10 : Module.{u2, u4} R M' _inst_1 _inst_9] {v' : α' -> M'} (f : Function.Embedding.{succ u1, succ u3} α α') (l : Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))), Eq.{succ u4} M' (coeFn.{max (succ (max u3 u2)) (succ u4), max (succ (max u3 u2)) (succ u4)} (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) (fun (_x : LinearMap.{u2, u2, max u3 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) => (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M') (LinearMap.hasCoeToFun.{u2, u2, max u3 u2, u4} R R (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u4, u2} α' M' R _inst_1 _inst_9 _inst_10 v') (Finsupp.embDomain.{u1, u3, u2} α α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) f l)) (coeFn.{max (succ (max u1 u2)) (succ u4), max (succ (max u1 u2)) (succ u4)} (LinearMap.{u2, u2, max u1 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) (fun (_x : LinearMap.{u2, u2, max u1 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) => (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M') (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u4} R R (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u1, u4, u2} α M' R _inst_1 _inst_9 _inst_10 (Function.comp.{succ u1, succ u3, succ u4} α α' M' v' (coeFn.{max 1 (succ u1) (succ u3), max (succ u1) (succ u3)} (Function.Embedding.{succ u1, succ u3} α α') (fun (_x : Function.Embedding.{succ u1, succ u3} α α') => α -> α') (Function.Embedding.hasCoeToFun.{succ u1, succ u3} α α') f))) l)
but is expected to have type
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+ forall {α : Type.{u4}} (R : Type.{u2}) {_inst_1 : Type.{u3}} {α' : Type.{u1}} [M' : Semiring.{u2} R] [_inst_9 : AddCommMonoid.{u1} α'] [_inst_10 : Module.{u2, u1} R α' M' _inst_9] {v' : _inst_1 -> α'} (f : Function.Embedding.{succ u4, succ u3} α _inst_1) (l : Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) => α') (Finsupp.embDomain.{u4, u3, u2} α _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M')) f l)) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R M' M' (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')) (Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) α' (Finsupp.addCommMonoid.{u3, u2} _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')))) _inst_9 (Finsupp.module.{u3, u2, u2} _inst_1 R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Semiring.toModule.{u2} R M')) _inst_10) (Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) (fun (_x : Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) => α') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) α' M' M' (Finsupp.addCommMonoid.{u3, u2} _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')))) _inst_9 (Finsupp.module.{u3, u2, u2} _inst_1 R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Semiring.toModule.{u2} R M')) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Finsupp.total.{u3, u1, u2} _inst_1 α' R M' _inst_9 _inst_10 v') (Finsupp.embDomain.{u4, u3, u2} α _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M')) f l)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u1), max (succ u4) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u4, u1} R R M' M' (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) α' (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')))) _inst_9 (Finsupp.module.{u4, u2, u2} α R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Semiring.toModule.{u2} R M')) _inst_10) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) (fun (_x : Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) => α') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u1} R R (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) α' M' M' (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')))) _inst_9 (Finsupp.module.{u4, u2, u2} α R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Semiring.toModule.{u2} R M')) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Finsupp.total.{u4, u1, u2} α α' R M' _inst_9 _inst_10 (Function.comp.{succ u4, succ u3, succ u1} α _inst_1 α' v' (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Function.Embedding.{succ u4, succ u3} α _inst_1) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => _inst_1) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u3), succ u4, succ u3} (Function.Embedding.{succ u4, succ u3} α _inst_1) α _inst_1 (Function.instEmbeddingLikeEmbedding.{succ u4, succ u3} α _inst_1)) f))) l)
Case conversion may be inaccurate. Consider using '#align finsupp.total_emb_domain Finsupp.total_embDomainₓ'. -/
@[simp]
theorem total_embDomain (f : α ↪ α') (l : α →₀ R) :
@@ -1083,7 +1083,7 @@ theorem total_embDomain (f : α ↪ α') (l : α →₀ R) :
lean 3 declaration is
forall {α : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] {α' : Type.{u3}} {M' : Type.{u4}} [_inst_9 : AddCommMonoid.{u4} M'] [_inst_10 : Module.{u2, u4} R M' _inst_1 _inst_9] {v' : α' -> M'} (f : α -> α') (l : Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))), Eq.{succ u4} M' (coeFn.{max (succ (max u3 u2)) (succ u4), max (succ (max u3 u2)) (succ u4)} (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) (fun (_x : LinearMap.{u2, u2, max u3 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) => (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M') (LinearMap.hasCoeToFun.{u2, u2, max u3 u2, u4} R R (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u4, u2} α' M' R _inst_1 _inst_9 _inst_10 v') (Finsupp.mapDomain.{u1, u3, u2} α α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f l)) (coeFn.{max (succ (max u1 u2)) (succ u4), max (succ (max u1 u2)) (succ u4)} (LinearMap.{u2, u2, max u1 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) (fun (_x : LinearMap.{u2, u2, max u1 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) => (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M') (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u4} R R (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u1, u4, u2} α M' R _inst_1 _inst_9 _inst_10 (Function.comp.{succ u1, succ u3, succ u4} α α' M' v' f)) l)
but is expected to have type
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+ forall {α : Type.{u4}} (R : Type.{u3}) {_inst_1 : Type.{u1}} {α' : Type.{u2}} [M' : Semiring.{u3} R] [_inst_9 : AddCommMonoid.{u2} α'] [_inst_10 : Module.{u3, u2} R α' M' _inst_9] {v' : _inst_1 -> α'} (f : α -> _inst_1) (l : Finsupp.{u4, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u1, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) => α') (Finsupp.mapDomain.{u4, u1, u3} α _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) f l)) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u1), succ u2} (LinearMap.{u3, u3, max u3 u1, u2} R R M' M' (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')) (Finsupp.{u1, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) α' (Finsupp.addCommMonoid.{u1, u3} _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')))) _inst_9 (Finsupp.module.{u1, u3, u3} _inst_1 R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) (Semiring.toModule.{u3} R M')) _inst_10) (Finsupp.{u1, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) (fun (_x : Finsupp.{u1, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u1, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) => α') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u1, u2} R R (Finsupp.{u1, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) α' M' M' (Finsupp.addCommMonoid.{u1, u3} _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')))) _inst_9 (Finsupp.module.{u1, u3, u3} _inst_1 R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) (Semiring.toModule.{u3} R M')) _inst_10 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) (Finsupp.total.{u1, u2, u3} _inst_1 α' R M' _inst_9 _inst_10 v') (Finsupp.mapDomain.{u4, u1, u3} α _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) f l)) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} R R M' M' (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')) (Finsupp.{u4, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) α' (Finsupp.addCommMonoid.{u4, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')))) _inst_9 (Finsupp.module.{u4, u3, u3} α R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) (Semiring.toModule.{u3} R M')) _inst_10) (Finsupp.{u4, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) (fun (_x : Finsupp.{u4, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u4, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) => α') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} R R (Finsupp.{u4, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) α' M' M' (Finsupp.addCommMonoid.{u4, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')))) _inst_9 (Finsupp.module.{u4, u3, u3} α R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) (Semiring.toModule.{u3} R M')) _inst_10 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) (Finsupp.total.{u4, u2, u3} α α' R M' _inst_9 _inst_10 (Function.comp.{succ u4, succ u1, succ u2} α _inst_1 α' v' f)) l)
Case conversion may be inaccurate. Consider using '#align finsupp.total_map_domain Finsupp.total_mapDomainₓ'. -/
@[simp]
theorem total_mapDomain (f : α → α') (l : α →₀ R) :
@@ -1095,7 +1095,7 @@ theorem total_mapDomain (f : α → α') (l : α →₀ R) :
lean 3 declaration is
forall {α : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] {α' : Type.{u3}} {M' : Type.{u4}} [_inst_9 : AddCommMonoid.{u4} M'] [_inst_10 : Module.{u2, u4} R M' _inst_1 _inst_9] {v' : α' -> M'} (f : Equiv.{succ u1, succ u3} α α') (l : Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))), Eq.{succ u4} M' (coeFn.{max (succ (max u3 u2)) (succ u4), max (succ (max u3 u2)) (succ u4)} (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) (fun (_x : LinearMap.{u2, u2, max u3 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) => (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M') (LinearMap.hasCoeToFun.{u2, u2, max u3 u2, u4} R R (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u4, u2} α' M' R _inst_1 _inst_9 _inst_10 v') (Finsupp.equivMapDomain.{u1, u3, u2} α α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) f l)) (coeFn.{max (succ (max u1 u2)) (succ u4), max (succ (max u1 u2)) (succ u4)} (LinearMap.{u2, u2, max u1 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) (fun (_x : LinearMap.{u2, u2, max u1 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) => (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M') (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u4} R R (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u1, u4, u2} α M' R _inst_1 _inst_9 _inst_10 (Function.comp.{succ u1, succ u3, succ u4} α α' M' v' (coeFn.{max 1 (max (succ u1) (succ u3)) (succ u3) (succ u1), max (succ u1) (succ u3)} (Equiv.{succ u1, succ u3} α α') (fun (_x : Equiv.{succ u1, succ u3} α α') => α -> α') (Equiv.hasCoeToFun.{succ u1, succ u3} α α') f))) l)
but is expected to have type
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+ forall {α : Type.{u4}} (R : Type.{u2}) {_inst_1 : Type.{u3}} {α' : Type.{u1}} [M' : Semiring.{u2} R] [_inst_9 : AddCommMonoid.{u1} α'] [_inst_10 : Module.{u2, u1} R α' M' _inst_9] {v' : _inst_1 -> α'} (f : Equiv.{succ u4, succ u3} α _inst_1) (l : Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) => α') (Finsupp.equivMapDomain.{u4, u3, u2} α _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M')) f l)) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R M' M' (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')) (Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) α' (Finsupp.addCommMonoid.{u3, u2} _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')))) _inst_9 (Finsupp.module.{u3, u2, u2} _inst_1 R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Semiring.toModule.{u2} R M')) _inst_10) (Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) (fun (_x : Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) => α') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) α' M' M' (Finsupp.addCommMonoid.{u3, u2} _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')))) _inst_9 (Finsupp.module.{u3, u2, u2} _inst_1 R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Semiring.toModule.{u2} R M')) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Finsupp.total.{u3, u1, u2} _inst_1 α' R M' _inst_9 _inst_10 v') (Finsupp.equivMapDomain.{u4, u3, u2} α _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M')) f l)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u1), max (succ u4) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u4, u1} R R M' M' (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) α' (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')))) _inst_9 (Finsupp.module.{u4, u2, u2} α R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Semiring.toModule.{u2} R M')) _inst_10) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) (fun (_x : Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) => α') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u1} R R (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) α' M' M' (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')))) _inst_9 (Finsupp.module.{u4, u2, u2} α R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Semiring.toModule.{u2} R M')) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Finsupp.total.{u4, u1, u2} α α' R M' _inst_9 _inst_10 (Function.comp.{succ u4, succ u3, succ u1} α _inst_1 α' v' (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Equiv.{succ u4, succ u3} α _inst_1) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => _inst_1) _x) (Equiv.instFunLikeEquiv.{succ u4, succ u3} α _inst_1) f))) l)
Case conversion may be inaccurate. Consider using '#align finsupp.total_equiv_map_domain Finsupp.total_equivMapDomainₓ'. -/
@[simp]
theorem total_equivMapDomain (f : α ≃ α') (l : α →₀ R) :
@@ -1118,7 +1118,7 @@ theorem span_eq_range_total (s : Set M) : span R s = (Finsupp.total s M R coe).r
lean 3 declaration is
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but is expected to have type
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+ forall {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u2} M) (x : M), Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 s)) (Exists.{max (succ u2) (succ u1)} (Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (l : Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} (Set.Elem.{u2} M s) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u1, u1} (Set.Elem.{u2} M s) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u2} R R (Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} (Set.Elem.{u2} M s) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u1, u1} (Set.Elem.{u2} M s) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} (Set.Elem.{u2} M s) M R _inst_1 _inst_3 _inst_4 (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s))) l) x))
Case conversion may be inaccurate. Consider using '#align finsupp.mem_span_iff_total Finsupp.mem_span_iff_totalₓ'. -/
theorem mem_span_iff_total (s : Set M) (x : M) :
x ∈ span R s ↔ ∃ l : s →₀ R, Finsupp.total s M R coe l = x :=
@@ -1170,7 +1170,7 @@ theorem span_image_eq_map_total (s : Set α) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {v : α -> M} {s : Set.{u1} α} {x : M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u3, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s))) (Exists.{succ (max u1 u3)} (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (fun (l : Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) => Exists.{0} (Membership.Mem.{max u1 u3, max u1 u3} (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (SetLike.hasMem.{max u1 u3, max u1 u3} (Submodule.{u3, max u1 u3} R 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u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)))) l (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s)) (fun (H : Membership.Mem.{max u1 u3, max u1 u3} (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (SetLike.hasMem.{max u1 u3, max u1 u3} (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) (Submodule.setLike.{u3, max 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v) l) x)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {v : α -> M} {s : Set.{u3} α} {x : M}, Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (Exists.{succ (max u3 u1)} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (fun (l : Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) => And (Membership.mem.{max u3 u1, max u1 u3} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{max u3 u1, max u3 u1} (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.setLike.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) l (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u1), succ u2} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (a : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) a) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 v) l) x)))
+ forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {v : α -> M} {s : Set.{u3} α} {x : M}, Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (Exists.{succ (max u3 u1)} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (fun (l : Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) => And (Membership.mem.{max u3 u1, max u1 u3} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{max u3 u1, max u3 u1} (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.setLike.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) l (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u1), succ u2} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (a : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) a) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 v) l) x)))
Case conversion may be inaccurate. Consider using '#align finsupp.mem_span_image_iff_total Finsupp.mem_span_image_iff_totalₓ'. -/
theorem mem_span_image_iff_total {s : Set α} {x : M} :
x ∈ span R (v '' s) ↔ ∃ l ∈ supported R R s, Finsupp.total α M R v l = x :=
@@ -1183,7 +1183,7 @@ theorem mem_span_image_iff_total {s : Set α} {x : M} :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (v : (Option.{u1} α) -> M) (f : Finsupp.{u1, u3} (Option.{u1} α) R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} (Option.{u1} α) R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} (Option.{u1} α) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} (Option.{u1} α) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} (Option.{u1} α) R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} (Option.{u1} α) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} (Option.{u1} α) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} (Option.{u1} α) R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} (Option.{u1} α) R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} (Option.{u1} α) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} (Option.{u1} α) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} (Option.{u1} α) M R _inst_1 _inst_3 _inst_4 v) f) (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M 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but is expected to have type
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+ forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (v : (Option.{u3} α) -> M) (f : Finsupp.{u3, u2} (Option.{u3} α) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} (Option.{u3} α) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) f) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} (Option.{u3} α) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} (Option.{u3} α) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R 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Case conversion may be inaccurate. Consider using '#align finsupp.total_option Finsupp.total_optionₓ'. -/
theorem total_option (v : Option α → M) (f : Option α →₀ R) :
Finsupp.total (Option α) M R v f =
@@ -1195,7 +1195,7 @@ theorem total_option (v : Option α → M) (f : Option α →₀ R) :
lean 3 declaration is
forall {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {α : Type.{u3}} {β : Type.{u4}} (A : α -> M) (B : β -> (Finsupp.{u3, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (f : Finsupp.{u4, u2} β R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))), Eq.{succ u1} M (coeFn.{max (succ (max u3 u2)) (succ u1), max (succ (max u3 u2)) (succ u1)} (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R 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+ forall {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {α : Type.{u4}} {β : Type.{u3}} (A : α -> M) (B : β -> (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))) (f : Finsupp.{u3, u2} β R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u3), max (succ u2) (succ u4)} (LinearMap.{u2, u2, max u2 u3, max u2 u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} β R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Finsupp.module.{u4, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, max u2 u4, u2} β (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) R _inst_1 (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u4, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} β R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Finsupp.module.{u4, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, max u2 u4, u2} β (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) R 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Case conversion may be inaccurate. Consider using '#align finsupp.total_total Finsupp.total_totalₓ'. -/
theorem total_total {α β : Type _} (A : α → M) (B : β → α →₀ R) (f : β →₀ R) :
Finsupp.total α M R A (Finsupp.total β (α →₀ R) R B f) =
@@ -1273,7 +1273,7 @@ theorem total_comp (f : α' → α) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {α' : Type.{u4}} {v : α -> M} (f : α -> α') (l : Finsupp.{u4, u3} α' R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (hf : Set.InjOn.{u1, u4} α α' f (Set.preimage.{u1, u4} α α' f ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} α') (Set.{u4} α') (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} α') (Set.{u4} α') (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} α') (Set.{u4} α') (Finset.Set.hasCoeT.{u4} α'))) (Finsupp.support.{u4, u3} α' R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) l)))), Eq.{succ u2} M 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(MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v) (Finsupp.comapDomain.{u1, u4, u3} α α' R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) f l hf)) (Finset.sum.{u2, u1} M α _inst_3 (Finset.preimage.{u1, u4} α α' (Finsupp.support.{u4, u3} α' R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) l) f hf) (fun (i : α) => SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) (coeFn.{max (succ u4) (succ u3), max (succ 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but is expected to have type
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+ forall {α : Type.{u2}} {M : Type.{u1}} (R : Type.{u3}) {_inst_1 : Type.{u4}} [_inst_3 : Semiring.{u3} R] [_inst_4 : AddCommMonoid.{u1} M] [α' : Module.{u3, u1} R M _inst_3 _inst_4] {v : α -> M} (f : α -> _inst_1) (l : Finsupp.{u4, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) (hf : Set.InjOn.{u2, u4} α _inst_1 f (Set.preimage.{u2, u4} α _inst_1 f (Finset.toSet.{u4} _inst_1 (Finsupp.support.{u4, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3)) l)))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u2, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) => M) (Finsupp.comapDomain.{u2, u4, u3} α _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3)) f l hf)) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_3 _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3)) (Finsupp.{u2, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) M (Finsupp.addCommMonoid.{u2, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3)))) _inst_4 (Finsupp.module.{u2, u3, u3} α R R _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3))) (Semiring.toModule.{u3} R _inst_3)) α') (Finsupp.{u2, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) (fun (_x : Finsupp.{u2, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u2, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) => M) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u1} R R (Finsupp.{u2, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) M _inst_3 _inst_3 (Finsupp.addCommMonoid.{u2, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3)))) _inst_4 (Finsupp.module.{u2, u3, u3} α R R _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3))) (Semiring.toModule.{u3} R _inst_3)) α' (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3))) (Finsupp.total.{u2, u1, u3} α M R _inst_3 _inst_4 α' v) (Finsupp.comapDomain.{u2, u4, u3} α _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3)) f l hf)) (Finset.sum.{u1, u2} M α _inst_4 (Finset.preimage.{u2, u4} α _inst_1 (Finsupp.support.{u4, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3)) l) f hf) (fun (i : α) => HSMul.hSMul.{u3, u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) M M (instHSMul.{u3, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) M (SMulZeroClass.toSMul.{u3, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u3, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) M (MonoidWithZero.toZero.{u3} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) _inst_3)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u3, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) M (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) _inst_3) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (Module.toMulActionWithZero.{u3, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) M _inst_3 _inst_4 α'))))) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Finsupp.{u4, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) _inst_1 (fun (_x : _inst_1) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) _x) (Finsupp.funLike.{u4, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) l (f i)) (v i)))
Case conversion may be inaccurate. Consider using '#align finsupp.total_comap_domain Finsupp.total_comapDomainₓ'. -/
theorem total_comapDomain (f : α → α') (l : α' →₀ R) (hf : Set.InjOn f (f ⁻¹' ↑l.support)) :
Finsupp.total α M R v (Finsupp.comapDomain f l hf) =
@@ -1285,7 +1285,7 @@ theorem total_comapDomain (f : α → α') (l : α' →₀ R) (hf : Set.InjOn f
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {s : Finset.{u1} α} {f : α -> R} (g : α -> M) (hf : forall (a : α), (Ne.{succ u3} R (f a) (OfNat.ofNat.{u3} R 0 (OfNat.mk.{u3} R 0 (Zero.zero.{u3} R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))))) -> (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s)), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 g) (Finsupp.onFinset.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) s f hf)) (Finset.sum.{u2, u1} M α _inst_3 s (fun (x : α) => SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) (f x) (g x)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {s : Finset.{u3} α} {f : α -> R} (g : α -> M) (hf : forall (a : α), (Ne.{succ u2} R (f a) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))))) -> (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) (Finsupp.onFinset.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) s f hf)) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 g) (Finsupp.onFinset.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) s f hf)) (Finset.sum.{u1, u3} M α _inst_3 s (fun (x : α) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4))))) (f x) (g x)))
+ forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {s : Finset.{u3} α} {f : α -> R} (g : α -> M) (hf : forall (a : α), (Ne.{succ u2} R (f a) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))))) -> (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) (Finsupp.onFinset.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) s f hf)) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 g) (Finsupp.onFinset.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) s f hf)) (Finset.sum.{u1, u3} M α _inst_3 s (fun (x : α) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4))))) (f x) (g x)))
Case conversion may be inaccurate. Consider using '#align finsupp.total_on_finset Finsupp.total_onFinsetₓ'. -/
theorem total_onFinset {s : Finset α} {f : α → R} (g : α → M) (hf : ∀ a, f a ≠ 0 → a ∈ s) :
Finsupp.total α M R g (Finsupp.onFinset s f hf) = Finset.sum s fun x : α => f x • g x :=
@@ -1318,7 +1318,7 @@ protected def domLCongr {α₁ α₂ : Type _} (e : α₁ ≃ α₂) : (α₁
lean 3 declaration is
forall {M : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {α₁ : Type.{u3}} {α₂ : Type.{u4}} (e : Equiv.{succ u3, succ u4} α₁ α₂) (v : Finsupp.{u3, u1} α₁ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))), Eq.{max (succ u4) (succ u1)} (Finsupp.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (coeFn.{max (succ (max u3 u1)) (succ (max u4 u1)), max (succ (max u3 u1)) (succ (max u4 u1))} (LinearEquiv.{u2, u2, max u3 u1, max u4 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (Finsupp.{u3, u1} α₁ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.addCommMonoid.{u3, u1} α₁ M _inst_3) (Finsupp.addCommMonoid.{u4, u1} α₂ M _inst_3) (Finsupp.module.{u3, u1, u2} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u1, u2} α₂ M R _inst_1 _inst_3 _inst_4)) (fun (_x : LinearEquiv.{u2, u2, max u3 u1, max u4 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (Finsupp.{u3, u1} α₁ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.addCommMonoid.{u3, u1} α₁ M _inst_3) (Finsupp.addCommMonoid.{u4, u1} α₂ M _inst_3) 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but is expected to have type
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+ forall {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {α₁ : Type.{u4}} {α₂ : Type.{u3}} (e : Equiv.{succ u4, succ u3} α₁ α₂) (v : Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))), Eq.{max (succ u2) (succ u3)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) v) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u2), max (succ u3) (succ u2)} (LinearEquiv.{u1, u1, max u2 u4, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{u4, u2} α₁ M 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u2} α₁ α₂ M _inst_3 e) v)
Case conversion may be inaccurate. Consider using '#align finsupp.dom_lcongr_apply Finsupp.domLCongr_applyₓ'. -/
@[simp]
theorem domLCongr_apply {α₁ : Type _} {α₂ : Type _} (e : α₁ ≃ α₂) (v : α₁ →₀ M) :
@@ -1365,7 +1365,7 @@ theorem domLCongr_symm {α₁ α₂ : Type _} (f : α₁ ≃ α₂) :
lean 3 declaration is
forall {M : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {α₁ : Type.{u3}} {α₂ : Type.{u4}} (e : Equiv.{succ u3, succ u4} α₁ α₂) (i : α₁) (m : M), Eq.{max (succ u4) (succ u1)} (Finsupp.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (coeFn.{max (succ (max u3 u1)) (succ (max u4 u1)), max (succ (max u3 u1)) (succ (max u4 u1))} (LinearEquiv.{u2, u2, max u3 u1, max u4 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (Finsupp.{u3, u1} α₁ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.addCommMonoid.{u3, u1} α₁ M _inst_3) (Finsupp.addCommMonoid.{u4, u1} α₂ M _inst_3) (Finsupp.module.{u3, u1, u2} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u1, u2} α₂ M R _inst_1 _inst_3 _inst_4)) (fun (_x : LinearEquiv.{u2, u2, max u3 u1, max u4 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (Finsupp.{u3, u1} α₁ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.addCommMonoid.{u3, u1} α₁ M _inst_3) (Finsupp.addCommMonoid.{u4, u1} α₂ M _inst_3) (Finsupp.module.{u3, u1, u2} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u1, u2} α₂ M R _inst_1 _inst_3 _inst_4)) => (Finsupp.{u3, u1} α₁ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) -> (Finsupp.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (LinearEquiv.hasCoeToFun.{u2, u2, max u3 u1, max u4 u1} R R (Finsupp.{u3, u1} α₁ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α₁ M _inst_3) (Finsupp.addCommMonoid.{u4, u1} α₂ M _inst_3) (Finsupp.module.{u3, u1, u2} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u1, u2} α₂ M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1)) (Finsupp.domLCongr.{u1, u2, u3, u4} M R _inst_1 _inst_3 _inst_4 α₁ α₂ e) (Finsupp.single.{u3, u1} α₁ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) i m)) (Finsupp.single.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (coeFn.{max 1 (max (succ u3) (succ u4)) (succ u4) (succ u3), max (succ u3) (succ u4)} (Equiv.{succ u3, succ u4} α₁ α₂) (fun (_x : Equiv.{succ u3, succ u4} α₁ α₂) => α₁ -> α₂) (Equiv.hasCoeToFun.{succ u3, succ u4} α₁ α₂) e i) m)
but is expected to have type
- forall {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {α₁ : Type.{u4}} {α₂ : Type.{u3}} (e : Equiv.{succ u4, succ u3} α₁ α₂) (i : α₁) (m : M), Eq.{max (succ u2) (succ u3)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.single.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) i m)) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u2), max (succ u3) (succ u2)} (LinearEquiv.{u1, u1, max u2 u4, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{u4, 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(LinearEquiv.{u1, u1, max u2 u4, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4)) R (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u4 u2} (Finsupp.{u4, u2} α₁ M 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(Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (LinearEquiv.{u1, u1, max u2 u4, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4)) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u4 u2, max u3 u2, max (max u4 u3) u2} R R (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (LinearEquiv.{u1, u1, max u2 u4, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4)) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u4 u2, max u3 u2} R R (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1)))))) (Finsupp.domLCongr.{u2, u1, u4, u3} M R _inst_1 _inst_3 _inst_4 α₁ α₂ e) (Finsupp.single.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) i m)) (Finsupp.single.{u3, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α₁) => α₂) i) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Equiv.{succ u4, succ u3} α₁ α₂) α₁ (fun (_x : α₁) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α₁) => α₂) _x) (Equiv.instFunLikeEquiv.{succ u4, succ u3} α₁ α₂) e i) m)
+ forall {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {α₁ : Type.{u4}} {α₂ : Type.{u3}} (e : Equiv.{succ u4, succ u3} α₁ α₂) (i : α₁) (m : M), Eq.{max (succ u2) (succ u3)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.single.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) i m)) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u2), max (succ u3) (succ u2)} (LinearEquiv.{u1, u1, max u2 u4, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{u4, 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Case conversion may be inaccurate. Consider using '#align finsupp.dom_lcongr_single Finsupp.domLCongr_singleₓ'. -/
@[simp]
theorem domLCongr_single {α₁ : Type _} {α₂ : Type _} (e : α₁ ≃ α₂) (i : α₁) (m : M) :
@@ -1533,7 +1533,7 @@ def lcongr {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N) : (ι →
lean 3 declaration is
forall {M : Type.{u1}} {N : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : Module.{u3, u2} R N _inst_1 _inst_5] {ι : Type.{u4}} {κ : Type.{u5}} (e₁ : Equiv.{succ u4, succ u5} ι κ) (e₂ : LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (i : ι) (m : M), Eq.{max (succ u5) (succ u2)} (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) (coeFn.{max (succ (max u4 u1)) (succ (max u5 u2)), max (succ (max u4 u1)) (succ (max u5 u2))} (LinearEquiv.{u3, u3, max u4 u1, max u5 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) (Finsupp.addCommMonoid.{u4, u1} ι M _inst_3) (Finsupp.addCommMonoid.{u5, u2} κ N _inst_5) (Finsupp.module.{u4, u1, u3} ι M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u5, u2, u3} κ N R _inst_1 _inst_5 _inst_6)) (fun (_x : LinearEquiv.{u3, u3, max u4 u1, max u5 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) (Finsupp.addCommMonoid.{u4, u1} ι M _inst_3) (Finsupp.addCommMonoid.{u5, u2} κ N _inst_5) (Finsupp.module.{u4, u1, u3} ι M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u5, u2, u3} κ N R _inst_1 _inst_5 _inst_6)) => (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) -> (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))))) (LinearEquiv.hasCoeToFun.{u3, u3, max u4 u1, max u5 u2} R R (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u1} ι M _inst_3) (Finsupp.addCommMonoid.{u5, u2} κ N _inst_5) (Finsupp.module.{u4, u1, u3} ι M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u5, u2, u3} κ N R _inst_1 _inst_5 _inst_6) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)) (Finsupp.lcongr.{u1, u2, u3, u4, u5} M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 ι κ e₁ e₂) (Finsupp.single.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) i m)) (Finsupp.single.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))) (coeFn.{max 1 (max (succ u4) (succ u5)) (succ u5) (succ u4), max (succ u4) (succ u5)} (Equiv.{succ u4, succ u5} ι κ) (fun (_x : Equiv.{succ u4, succ u5} ι κ) => ι -> κ) (Equiv.hasCoeToFun.{succ u4, succ u5} ι κ) e₁ i) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (_x : LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) => M -> N) (LinearEquiv.hasCoeToFun.{u3, u3, u1, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)) e₂ m))
but is expected to have type
- forall {M : Type.{u2}} {N : Type.{u1}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : Module.{u3, u1} R N _inst_1 _inst_5] {ι : Type.{u5}} {κ : Type.{u4}} (e₁ : Equiv.{succ u5, succ u4} ι κ) (e₂ : LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (i : ι) (m : M), Eq.{max (succ u1) (succ u4)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (Finsupp.single.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) i m)) 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(SMulZeroClass.toSMul.{u3, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (DistribSMul.toSMulZeroClass.{u3, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (DistribMulAction.toDistribSMul.{u3, u2} R M (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} M _inst_3) (Module.toDistribMulAction.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u3, u1} R N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5)) (DistribSMul.toSMulZeroClass.{u3, u1} R N (AddMonoid.toAddZeroClass.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5)) (DistribMulAction.toDistribSMul.{u3, u1} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_5) (Module.toDistribMulAction.{u3, u1} R N _inst_1 _inst_5 _inst_6)))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) R M N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} M _inst_3) (AddCommMonoid.toAddMonoid.{u1} N _inst_5) (Module.toDistribMulAction.{u3, u2} R M _inst_1 _inst_3 _inst_4) (Module.toDistribMulAction.{u3, u1} R N _inst_1 _inst_5 _inst_6) (SemilinearMapClass.distribMulActionHomClass.{u3, u2, u1, max u2 u1} R M N (LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 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+ forall {M : Type.{u2}} {N : Type.{u1}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : Module.{u3, u1} R N _inst_1 _inst_5] {ι : Type.{u5}} {κ : Type.{u4}} (e₁ : Equiv.{succ u5, succ u4} ι κ) (e₂ : LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (i : ι) (m : M), Eq.{max (succ u1) (succ u4)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (Finsupp.single.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) i m)) 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(SemilinearEquivClass.instSemilinearMapClass.{u3, u3, u2, u1, max u2 u1} R R M N (LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, u2, u1} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)))))) e₂ m))
Case conversion may be inaccurate. Consider using '#align finsupp.lcongr_single Finsupp.lcongr_singleₓ'. -/
@[simp]
theorem lcongr_single {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N) (i : ι) (m : M) :
@@ -1544,7 +1544,7 @@ theorem lcongr_single {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N)
lean 3 declaration is
forall {M : Type.{u1}} {N : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : Module.{u3, u2} R N _inst_1 _inst_5] {ι : Type.{u4}} {κ : Type.{u5}} (e₁ : Equiv.{succ u4, succ u5} ι κ) (e₂ : LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (f : Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (k : κ), Eq.{succ u2} N (coeFn.{max (succ u5) (succ u2), max (succ u5) (succ u2)} (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) (fun (_x : Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) => κ -> N) (Finsupp.coeFun.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) (coeFn.{max (succ (max u4 u1)) (succ (max u5 u2)), max (succ (max u4 u1)) (succ (max u5 u2))} (LinearEquiv.{u3, u3, max u4 u1, max u5 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) (Finsupp.addCommMonoid.{u4, u1} ι M _inst_3) (Finsupp.addCommMonoid.{u5, u2} κ N _inst_5) (Finsupp.module.{u4, u1, u3} ι M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u5, u2, u3} κ N R _inst_1 _inst_5 _inst_6)) (fun (_x : LinearEquiv.{u3, u3, max u4 u1, max u5 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) (Finsupp.addCommMonoid.{u4, u1} ι M _inst_3) (Finsupp.addCommMonoid.{u5, u2} κ N _inst_5) (Finsupp.module.{u4, u1, u3} ι M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u5, u2, u3} κ N R _inst_1 _inst_5 _inst_6)) => (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) -> (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))))) (LinearEquiv.hasCoeToFun.{u3, u3, max u4 u1, max u5 u2} R R (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u1} ι M _inst_3) (Finsupp.addCommMonoid.{u5, u2} κ N _inst_5) (Finsupp.module.{u4, u1, u3} ι M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u5, u2, u3} κ N R _inst_1 _inst_5 _inst_6) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)) (Finsupp.lcongr.{u1, u2, u3, u4, u5} M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 ι κ e₁ e₂) f) k) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (_x : LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) => M -> N) (LinearEquiv.hasCoeToFun.{u3, u3, u1, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)) e₂ (coeFn.{max (succ u4) (succ u1), max (succ u4) (succ u1)} (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (fun (_x : Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) => ι -> M) (Finsupp.coeFun.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) f (coeFn.{max 1 (max (succ u5) (succ u4)) (succ u4) (succ u5), max (succ u5) (succ u4)} (Equiv.{succ u5, succ u4} κ ι) (fun (_x : Equiv.{succ u5, succ u4} κ ι) => κ -> ι) (Equiv.hasCoeToFun.{succ u5, succ u4} κ ι) (Equiv.symm.{succ u4, succ u5} ι κ e₁) k)))
but is expected to have type
- forall {M : Type.{u2}} {N : Type.{u1}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : Module.{u3, u1} R N _inst_1 _inst_5] {ι : Type.{u5}} {κ : Type.{u4}} (e₁ : Equiv.{succ u5, succ u4} ι κ) (e₂ : LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (f : Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (k : κ), Eq.{succ u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : κ) => N) k) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) κ (fun (_x : κ) => (fun 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(AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u5, u2} ι M _inst_3) (Finsupp.addCommMonoid.{u4, u1} κ N _inst_5) (Finsupp.module.{u5, u2, u3} ι M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u1, u3} κ N R _inst_1 _inst_5 _inst_6) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)))))) (Finsupp.lcongr.{u2, u1, u3, u5, u4} M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 ι κ e₁ e₂) f) k) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M) => N) _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) R M N (SMulZeroClass.toSMul.{u3, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (DistribSMul.toSMulZeroClass.{u3, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (DistribMulAction.toDistribSMul.{u3, u2} R M (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} M _inst_3) (Module.toDistribMulAction.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u3, u1} R N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5)) (DistribSMul.toSMulZeroClass.{u3, u1} R N (AddMonoid.toAddZeroClass.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5)) (DistribMulAction.toDistribSMul.{u3, u1} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_5) (Module.toDistribMulAction.{u3, u1} R N _inst_1 _inst_5 _inst_6)))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) R M N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} M _inst_3) (AddCommMonoid.toAddMonoid.{u1} N _inst_5) (Module.toDistribMulAction.{u3, u2} R M _inst_1 _inst_3 _inst_4) 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(Equiv.symm.{succ u5, succ u4} ι κ e₁) k)))
+ forall {M : Type.{u2}} {N : Type.{u1}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : Module.{u3, u1} R N _inst_1 _inst_5] {ι : Type.{u5}} {κ : Type.{u4}} (e₁ : Equiv.{succ u5, succ u4} ι κ) (e₂ : LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (f : Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (k : κ), Eq.{succ u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : κ) => N) k) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) κ (fun (_x : κ) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : κ) => N) _x) (Finsupp.funLike.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (FunLike.coe.{max (max (max (succ u2) (succ u1)) (succ u5)) (succ u4), max (succ u2) (succ u5), max (succ u1) (succ u4)} (LinearEquiv.{u3, u3, max u2 u5, max u1 u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (Finsupp.addCommMonoid.{u5, u2} ι M _inst_3) (Finsupp.addCommMonoid.{u4, u1} κ N _inst_5) (Finsupp.module.{u5, u2, u3} ι M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u1, u3} κ N R _inst_1 _inst_5 _inst_6)) (Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M 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(AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u5, u2} ι M _inst_3) (Finsupp.addCommMonoid.{u4, u1} κ N _inst_5) (Finsupp.module.{u5, u2, u3} ι M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u1, u3} κ N R _inst_1 _inst_5 _inst_6) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)))))) (Finsupp.lcongr.{u2, u1, u3, u5, u4} M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 ι κ e₁ e₂) f) k) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : M) => N) _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) R M N (SMulZeroClass.toSMul.{u3, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (DistribSMul.toSMulZeroClass.{u3, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (DistribMulAction.toDistribSMul.{u3, u2} R M (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} M _inst_3) (Module.toDistribMulAction.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u3, u1} R N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5)) (DistribSMul.toSMulZeroClass.{u3, u1} R N (AddMonoid.toAddZeroClass.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5)) (DistribMulAction.toDistribSMul.{u3, u1} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_5) (Module.toDistribMulAction.{u3, u1} R N _inst_1 _inst_5 _inst_6)))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) R M N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} M _inst_3) (AddCommMonoid.toAddMonoid.{u1} N _inst_5) (Module.toDistribMulAction.{u3, u2} R M _inst_1 _inst_3 _inst_4) 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(Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, u2, u1} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)))))) e₂ (FunLike.coe.{max (succ u5) (succ u2), succ u5, succ u2} (Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => M) _x) (Finsupp.funLike.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) f (FunLike.coe.{max (succ u5) (succ u4), succ u4, succ u5} (Equiv.{succ u4, succ u5} κ ι) κ (fun (_x : κ) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : κ) => ι) _x) (Equiv.instFunLikeEquiv.{succ u4, succ u5} κ ι) (Equiv.symm.{succ u5, succ u4} ι κ e₁) k)))
Case conversion may be inaccurate. Consider using '#align finsupp.lcongr_apply_apply Finsupp.lcongr_apply_applyₓ'. -/
@[simp]
theorem lcongr_apply_apply {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N) (f : ι →₀ M) (k : κ) :
@@ -1556,7 +1556,7 @@ theorem lcongr_apply_apply {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[
lean 3 declaration is
forall {M : Type.{u1}} {N : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : Module.{u3, u2} R N _inst_1 _inst_5] {ι : Type.{u4}} {κ : Type.{u5}} (e₁ : Equiv.{succ u4, succ u5} ι κ) (e₂ : LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (k : κ) (n : N), Eq.{max (succ u4) (succ u1)} (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (coeFn.{max (succ (max u5 u2)) (succ (max u4 u1)), max (succ (max u5 u2)) (succ (max u4 u1))} (LinearEquiv.{u3, u3, max u5 u2, max u4 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R 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but is expected to have type
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(LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) N M _inst_5 _inst_3 _inst_6 _inst_4) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : N) => M) _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u1, u2} (LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) N M _inst_5 _inst_3 _inst_6 _inst_4) R N M (SMulZeroClass.toSMul.{u3, u1} R N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5)) (DistribSMul.toSMulZeroClass.{u3, u1} R N (AddMonoid.toAddZeroClass.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5)) (DistribMulAction.toDistribSMul.{u3, u1} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_5) (Module.toDistribMulAction.{u3, u1} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u3, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (DistribSMul.toSMulZeroClass.{u3, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (DistribMulAction.toDistribSMul.{u3, u2} R M (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} M _inst_3) (Module.toDistribMulAction.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u1, u2} (LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) N M _inst_5 _inst_3 _inst_6 _inst_4) R N M (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_5) (AddCommMonoid.toAddMonoid.{u2} M _inst_3) (Module.toDistribMulAction.{u3, u1} R N _inst_1 _inst_5 _inst_6) (Module.toDistribMulAction.{u3, u2} R M _inst_1 _inst_3 _inst_4) (SemilinearMapClass.distribMulActionHomClass.{u3, u1, u2, max u2 u1} R N M (LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) N M _inst_5 _inst_3 _inst_6 _inst_4) _inst_1 _inst_5 _inst_3 _inst_6 _inst_4 (SemilinearEquivClass.instSemilinearMapClass.{u3, u3, u1, u2, max u2 u1} R R N M (LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) 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+ forall {M : Type.{u2}} {N : Type.{u1}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : Module.{u3, u1} R N _inst_1 _inst_5] {ι : Type.{u5}} {κ : Type.{u4}} (e₁ : Equiv.{succ u5, succ u4} ι κ) (e₂ : LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (k : κ) (n : N), Eq.{max (succ u2) (succ u5)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) => Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.single.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5)) k n)) 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(Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.lcongr.{u2, u1, u3, u5, u4} M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 ι κ e₁ e₂)) (Finsupp.single.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5)) k n)) (Finsupp.single.{u5, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : κ) => ι) k) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : N) => M) n) (AddMonoid.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : N) => M) n) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : N) => M) n) _inst_3)) (FunLike.coe.{max (succ u4) (succ u5), succ u4, succ u5} (Equiv.{succ u4, succ u5} κ ι) κ (fun (_x : κ) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : κ) => ι) _x) (Equiv.instFunLikeEquiv.{succ u4, succ u5} κ ι) (Equiv.symm.{succ u5, succ u4} ι κ e₁) k) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} 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M (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_5) (AddCommMonoid.toAddMonoid.{u2} M _inst_3) (Module.toDistribMulAction.{u3, u1} R N _inst_1 _inst_5 _inst_6) (Module.toDistribMulAction.{u3, u2} R M _inst_1 _inst_3 _inst_4) (SemilinearMapClass.distribMulActionHomClass.{u3, u1, u2, max u2 u1} R N M (LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) N M _inst_5 _inst_3 _inst_6 _inst_4) _inst_1 _inst_5 _inst_3 _inst_6 _inst_4 (SemilinearEquivClass.instSemilinearMapClass.{u3, u3, u1, u2, max u2 u1} R R N M (LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) 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Case conversion may be inaccurate. Consider using '#align finsupp.lcongr_symm_single Finsupp.lcongr_symm_singleₓ'. -/
theorem lcongr_symm_single {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N) (k : κ) (n : N) :
(lcongr e₁ e₂).symm (Finsupp.single k n) = Finsupp.single (e₁.symm k) (e₂.symm n) :=
@@ -1607,7 +1607,7 @@ def sumFinsuppLEquivProdFinsupp {α β : Type _} : (Sum α β →₀ M) ≃ₗ[R
lean 3 declaration is
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M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Prod.instAddCommMonoidSum.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} β M _inst_3)))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} R (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M 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_inst_1 _inst_3 _inst_4))) R (Finsupp.{max u3 u4, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (Finsupp.{max u3 u4, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{max u4 u3, u2} (Sum.{u4, u3} α β) M _inst_3)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Prod.instAddCommMonoidSum.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α 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(Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (LinearEquiv.{u1, u1, max u2 u3 u4, max (max u2 u3) u2 u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{max u3 u4, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.addCommMonoid.{max u4 u3, u2} (Sum.{u4, u3} α β) M _inst_3) (Prod.instAddCommMonoidSum.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M 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+ forall {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {α : Type.{u4}} {β : Type.{u3}} (f : Finsupp.{max u3 u4, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (x : α), Eq.{succ u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) x) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) α (fun (_x : α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) _x) (Finsupp.funLike.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Prod.fst.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (max (succ 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_inst_3))) _inst_1 (Finsupp.addCommMonoid.{max u4 u3, u2} (Sum.{u4, u3} α β) M _inst_3) (Finsupp.module.{max u4 u3, u2, u1} (Sum.{u4, u3} α β) M R _inst_1 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} R (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (AddMonoid.toZero.{max (max u3 u4) u2} (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Prod.instAddCommMonoidSum.{max u2 u4, max u2 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Case conversion may be inaccurate. Consider using '#align finsupp.fst_sum_finsupp_lequiv_prod_finsupp Finsupp.fst_sumFinsuppLEquivProdFinsuppₓ'. -/
theorem fst_sumFinsuppLEquivProdFinsupp {α β : Type _} (f : Sum α β →₀ M) (x : α) :
(sumFinsuppLEquivProdFinsupp R f).1 x = f (Sum.inl x) :=
@@ -1618,7 +1618,7 @@ theorem fst_sumFinsuppLEquivProdFinsupp {α β : Type _} (f : Sum α β →₀ M
lean 3 declaration is
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but is expected to have type
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M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Prod.instAddCommMonoidSum.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} β M _inst_3)))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} R (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M 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_inst_1 _inst_3 _inst_4))) R (Finsupp.{max u3 u4, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (Finsupp.{max u3 u4, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{max u4 u3, u2} (Sum.{u4, u3} α β) M _inst_3)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Prod.instAddCommMonoidSum.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α 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Case conversion may be inaccurate. Consider using '#align finsupp.snd_sum_finsupp_lequiv_prod_finsupp Finsupp.snd_sumFinsuppLEquivProdFinsuppₓ'. -/
theorem snd_sumFinsuppLEquivProdFinsupp {α β : Type _} (f : Sum α β →₀ M) (y : β) :
(sumFinsuppLEquivProdFinsupp R f).2 y = f (Sum.inr y) :=
@@ -1629,7 +1629,7 @@ theorem snd_sumFinsuppLEquivProdFinsupp {α β : Type _} (f : Sum α β →₀ M
lean 3 declaration is
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but is expected to have type
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+ forall {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {α : Type.{u4}} {β : Type.{u3}} (fg : Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (x : α), Eq.{succ u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Sum.{u4, u3} α β) => M) (Sum.inl.{u4, u3} α β x)) (FunLike.coe.{max (succ (max u4 u3)) (succ u2), succ (max u4 u3), succ u2} (Finsupp.{max u4 u3, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Sum.{u4, u3} α β) (fun (_x : Sum.{u4, u3} α β) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Sum.{u4, u3} α β) => M) _x) (Finsupp.funLike.{max u4 u3, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (FunLike.coe.{max (max (succ u3) 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Case conversion may be inaccurate. Consider using '#align finsupp.sum_finsupp_lequiv_prod_finsupp_symm_inl Finsupp.sumFinsuppLEquivProdFinsupp_symm_inlₓ'. -/
theorem sumFinsuppLEquivProdFinsupp_symm_inl {α β : Type _} (fg : (α →₀ M) × (β →₀ M)) (x : α) :
((sumFinsuppLEquivProdFinsupp R).symm fg) (Sum.inl x) = fg.1 x :=
@@ -1640,7 +1640,7 @@ theorem sumFinsuppLEquivProdFinsupp_symm_inl {α β : Type _} (fg : (α →₀ M
lean 3 declaration is
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but is expected to have type
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(AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Prod.instAddCommMonoidSum.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} β M _inst_3)) (Finsupp.addCommMonoid.{max u4 u3, u2} (Sum.{u4, u3} α β) M _inst_3) (Prod.module.{u1, max u2 u4, max u2 u3} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} β M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} β M R _inst_1 _inst_3 _inst_4)) (Finsupp.module.{max u4 u3, u2, u1} (Sum.{u4, u3} α β) M R _inst_1 _inst_3 _inst_4)) 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+ forall {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {α : Type.{u4}} {β : Type.{u3}} (fg : Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (y : β), Eq.{succ u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Sum.{u4, u3} α β) => M) (Sum.inr.{u4, u3} α β y)) (FunLike.coe.{max (succ (max u4 u3)) (succ u2), succ (max u4 u3), succ u2} (Finsupp.{max u4 u3, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Sum.{u4, u3} α β) (fun (_x : Sum.{u4, u3} α β) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Sum.{u4, u3} α β) => M) _x) (Finsupp.funLike.{max u4 u3, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (FunLike.coe.{max (max (succ u3) 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u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Prod.instAddCommMonoidSum.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} β M _inst_3)))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} R (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Prod.instAddCommMonoidSum.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} β M _inst_3))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} R (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Prod.instAddCommMonoidSum.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M 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(AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (Finsupp.{max u3 u4, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{max u4 u3, u2} (Sum.{u4, u3} α β) M _inst_3)) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} R (Finsupp.{max u3 u4, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{max u4 u3, u2} (Sum.{u4, u3} α β) M _inst_3) (Finsupp.module.{max u4 u3, u2, u1} (Sum.{u4, u3} α β) M R _inst_1 _inst_3 _inst_4))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{max u3 u4, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Prod.instAddCommMonoidSum.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} β M _inst_3)) (Finsupp.addCommMonoid.{max u4 u3, u2} (Sum.{u4, u3} α β) M _inst_3) (Prod.module.{u1, max u2 u4, max u2 u3} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M 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_inst_4)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} R (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{max u3 u4, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (LinearEquiv.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{max u3 u4, u2} (Sum.{u4, u3} α β) M 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Case conversion may be inaccurate. Consider using '#align finsupp.sum_finsupp_lequiv_prod_finsupp_symm_inr Finsupp.sumFinsuppLEquivProdFinsupp_symm_inrₓ'. -/
theorem sumFinsuppLEquivProdFinsupp_symm_inr {α β : Type _} (fg : (α →₀ M) × (β →₀ M)) (y : β) :
((sumFinsuppLEquivProdFinsupp R).symm fg) (Sum.inr y) = fg.2 y :=
@@ -1677,7 +1677,7 @@ noncomputable def sigmaFinsuppLEquivPiFinsupp {M : Type _} {ιs : η → Type _}
lean 3 declaration is
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but is expected to have type
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(AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u1} (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (Finsupp.addCommMonoid.{max u1 u3, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M _inst_11)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u1} (forall (j : η), Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (Pi.addCommMonoid.{u1, max u4 u3} η (fun (j : η) => Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (fun (i : η) => Finsupp.addCommMonoid.{u3, u4} (ιs i) M _inst_11))) (Module.toDistribMulAction.{u2, max (max u3 u4) u1} R (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) _inst_1 (Finsupp.addCommMonoid.{max u1 u3, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M _inst_11) (Finsupp.module.{max u1 u3, u4, u2} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M R _inst_1 _inst_11 _inst_12)) (Module.toDistribMulAction.{u2, max (max u3 u4) u1} R (forall (j : η), Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) _inst_1 (Pi.addCommMonoid.{u1, max u4 u3} η (fun (j : η) => Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (fun (i : η) => Finsupp.addCommMonoid.{u3, u4} (ιs i) M _inst_11)) (Pi.module.{u1, max u4 u3, u2} η (fun (j : η) => Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) R _inst_1 (fun (i : η) => Finsupp.addCommMonoid.{u3, u4} (ιs i) M _inst_11) (fun (i : η) => Finsupp.module.{u3, u4, u2} (ιs i) M R _inst_1 _inst_11 _inst_12))) (SemilinearMapClass.distribMulActionHomClass.{u2, max (max u3 u4) u1, max (max u3 u4) u1, max 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Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) R _inst_1 (fun (i : η) => Finsupp.addCommMonoid.{u3, u4} (ιs i) M _inst_11) (fun (i : η) => Finsupp.module.{u3, u4, u2} (ιs i) M R _inst_1 _inst_11 _inst_12)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max (max u3 u4) u1, max (max u3 u4) u1, max (max u3 u4) u1} R R (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (forall (j : η), Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (LinearEquiv.{u2, u2, max u4 u3 u1, max (max u1 u4) u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M 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+ forall (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] {η : Type.{u1}} [_inst_9 : Fintype.{u1} η] {M : Type.{u4}} {ιs : η -> Type.{u3}} [_inst_11 : AddCommMonoid.{u4} M] [_inst_12 : Module.{u2, u4} R M _inst_1 _inst_11] (f : Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (j : η) (i : ιs j), Eq.{succ u4} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ιs j) => M) i) (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (ιs j) (fun (_x : ιs j) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ιs j) => M) _x) (Finsupp.funLike.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u1), max (max (succ u3) (succ u4)) (succ u1), max (max (succ u3) (succ u4)) (succ u1)} (LinearEquiv.{u2, u2, max u4 u3 u1, max (max u1 u4) 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_inst_1 (fun (i : η) => Finsupp.addCommMonoid.{u3, u4} (ιs i) M _inst_11) (fun (i : η) => Finsupp.module.{u3, u4, u2} (ιs i) M R _inst_1 _inst_11 _inst_12))) R (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (forall (j : η), Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (SMulZeroClass.toSMul.{u2, max (max u3 u4) u1} R (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (AddMonoid.toZero.{max (max u3 u4) u1} (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u1} (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (Finsupp.addCommMonoid.{max u1 u3, 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(AddCommMonoid.toAddMonoid.{max (max u3 u4) u1} (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (Finsupp.addCommMonoid.{max u1 u3, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M _inst_11)) (Module.toDistribMulAction.{u2, max (max u3 u4) u1} R (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) _inst_1 (Finsupp.addCommMonoid.{max u1 u3, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M _inst_11) (Finsupp.module.{max u1 u3, u4, u2} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M R _inst_1 _inst_11 _inst_12))))) (SMulZeroClass.toSMul.{u2, max (max u3 u4) u1} R (forall (j : η), Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (AddMonoid.toZero.{max (max u3 u4) u1} (forall (j : η), Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u1} (forall (j : η), Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (Pi.addCommMonoid.{u1, max u4 u3} η (fun (j : η) => Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (fun (i : η) => Finsupp.addCommMonoid.{u3, u4} (ιs i) M _inst_11)))) (DistribSMul.toSMulZeroClass.{u2, max (max u3 u4) u1} R (forall (j : η), Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (AddMonoid.toAddZeroClass.{max (max u3 u4) u1} (forall (j : η), Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u1} (forall (j : η), Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (Pi.addCommMonoid.{u1, max u4 u3} η (fun (j : η) => Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (fun (i : η) => Finsupp.addCommMonoid.{u3, u4} (ιs i) M _inst_11)))) (DistribMulAction.toDistribSMul.{u2, max (max u3 u4) u1} R (forall (j : η), Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u1} (forall (j : η), Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (Pi.addCommMonoid.{u1, max u4 u3} η (fun (j : η) => Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (fun (i : η) => Finsupp.addCommMonoid.{u3, u4} (ιs i) M _inst_11))) (Module.toDistribMulAction.{u2, max (max u3 u4) u1} R (forall (j : η), Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) _inst_1 (Pi.addCommMonoid.{u1, max u4 u3} η (fun (j : η) => Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (fun (i : η) => Finsupp.addCommMonoid.{u3, u4} (ιs i) M _inst_11)) (Pi.module.{u1, max u4 u3, u2} η (fun (j : η) => Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) R _inst_1 (fun (i : η) => Finsupp.addCommMonoid.{u3, u4} (ιs i) M _inst_11) (fun (i : η) => Finsupp.module.{u3, u4, u2} (ιs i) M R _inst_1 _inst_11 _inst_12)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u1, u2, max (max u3 u4) u1, max (max u3 u4) u1} (LinearEquiv.{u2, u2, max u4 u3 u1, max (max u1 u4) u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (forall (j : η), Finsupp.{u3, 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(AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u1} (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (Finsupp.addCommMonoid.{max u1 u3, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M _inst_11)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u1} (forall (j : η), Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (Pi.addCommMonoid.{u1, max u4 u3} η (fun (j : η) => Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (fun (i : η) => Finsupp.addCommMonoid.{u3, u4} (ιs i) M _inst_11))) (Module.toDistribMulAction.{u2, max (max u3 u4) u1} R (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) _inst_1 (Finsupp.addCommMonoid.{max u1 u3, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M _inst_11) (Finsupp.module.{max u1 u3, u4, u2} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M R _inst_1 _inst_11 _inst_12)) (Module.toDistribMulAction.{u2, max (max u3 u4) u1} R (forall (j : η), Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) _inst_1 (Pi.addCommMonoid.{u1, max u4 u3} η (fun (j : η) => Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (fun (i : η) => Finsupp.addCommMonoid.{u3, u4} (ιs i) M _inst_11)) (Pi.module.{u1, max u4 u3, u2} η (fun (j : η) => Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) R _inst_1 (fun (i : η) => Finsupp.addCommMonoid.{u3, u4} (ιs i) M _inst_11) (fun (i : η) => Finsupp.module.{u3, u4, u2} (ιs i) M R _inst_1 _inst_11 _inst_12))) (SemilinearMapClass.distribMulActionHomClass.{u2, max (max u3 u4) u1, max (max u3 u4) u1, max 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Case conversion may be inaccurate. Consider using '#align finsupp.sigma_finsupp_lequiv_pi_finsupp_apply Finsupp.sigmaFinsuppLEquivPiFinsupp_applyₓ'. -/
@[simp]
theorem sigmaFinsuppLEquivPiFinsupp_apply {M : Type _} {ιs : η → Type _} [AddCommMonoid M]
@@ -1689,7 +1689,7 @@ theorem sigmaFinsuppLEquivPiFinsupp_apply {M : Type _} {ιs : η → Type _} [Ad
lean 3 declaration is
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but is expected to have type
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R _inst_1 _inst_11 _inst_12)) (Finsupp.module.{max u1 u3, u4, u2} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M R _inst_1 _inst_11 _inst_12) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1)))))) (LinearEquiv.symm.{u2, u2, max (max u3 u4) u1, max (max u3 u4) u1} R R (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (forall (j : η), Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{max u1 u3, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M _inst_11) (Pi.addCommMonoid.{u1, max u4 u3} η (fun (j : η) => Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (fun (i : η) => Finsupp.addCommMonoid.{u3, u4} (ιs i) M _inst_11)) 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+ forall (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] {η : Type.{u1}} [_inst_9 : Fintype.{u1} η] {M : Type.{u4}} {ιs : η -> Type.{u3}} [_inst_11 : AddCommMonoid.{u4} M] [_inst_12 : Module.{u2, u4} R M _inst_1 _inst_11] (f : forall (j : η), Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (ji : Sigma.{u1, u3} η (fun (j : η) => ιs j)), Eq.{succ u4} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Sigma.{u1, u3} η (fun (j : η) => ιs j)) => M) ji) (FunLike.coe.{max (succ (max u1 u3)) (succ u4), succ (max u1 u3), succ u4} (Finsupp.{max u1 u3, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (Sigma.{u1, u3} η (fun (j : η) => ιs j)) (fun (_x : Sigma.{u1, u3} η (fun (j : η) => ιs j)) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Sigma.{u1, u3} η (fun (j : η) => ιs j)) => M) _x) (Finsupp.funLike.{max u1 u3, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} 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_inst_11)))) (DistribMulAction.toDistribSMul.{u2, max (max u3 u4) u1} R (forall (j : η), Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u1} (forall (j : η), Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (Pi.addCommMonoid.{u1, max u4 u3} η (fun (j : η) => Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (fun (i : η) => Finsupp.addCommMonoid.{u3, u4} (ιs i) M _inst_11))) (Module.toDistribMulAction.{u2, max (max u3 u4) u1} R (forall (j : η), Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) _inst_1 (Pi.addCommMonoid.{u1, max u4 u3} η (fun (j : η) => Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (fun (i : η) => Finsupp.addCommMonoid.{u3, u4} (ιs i) M _inst_11)) (Pi.module.{u1, max u4 u3, u2} η (fun (j : η) => Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) R _inst_1 (fun (i : η) => Finsupp.addCommMonoid.{u3, u4} (ιs i) M _inst_11) (fun (i : η) => Finsupp.module.{u3, u4, u2} (ιs i) M R _inst_1 _inst_11 _inst_12)))))) (SMulZeroClass.toSMul.{u2, max (max u3 u4) u1} R (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (AddMonoid.toZero.{max (max u3 u4) u1} (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u1} (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (Finsupp.addCommMonoid.{max u1 u3, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M _inst_11))) (DistribSMul.toSMulZeroClass.{u2, max (max u3 u4) u1} R (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (AddMonoid.toAddZeroClass.{max (max u3 u4) u1} (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u1} (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (Finsupp.addCommMonoid.{max u1 u3, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M _inst_11))) (DistribMulAction.toDistribSMul.{u2, max (max u3 u4) u1} R (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u1} (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (Finsupp.addCommMonoid.{max u1 u3, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M _inst_11)) (Module.toDistribMulAction.{u2, max (max u3 u4) u1} R (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) _inst_1 (Finsupp.addCommMonoid.{max u1 u3, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M _inst_11) (Finsupp.module.{max u1 u3, u4, u2} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M R _inst_1 _inst_11 _inst_12))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u1, u2, max (max u3 u4) u1, max (max u3 u4) u1} (LinearEquiv.{u2, u2, max (max u3 u4) u1, max (max u3 u4) u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) 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_inst_12)) R (forall (j : η), Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u1} (forall (j : η), Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (Pi.addCommMonoid.{u1, max u4 u3} η (fun (j : η) => Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (fun (i : η) => Finsupp.addCommMonoid.{u3, u4} (ιs i) M _inst_11))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u1} (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (Finsupp.addCommMonoid.{max u1 u3, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M _inst_11)) (Module.toDistribMulAction.{u2, max (max u3 u4) u1} R (forall (j : η), Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) _inst_1 (Pi.addCommMonoid.{u1, max u4 u3} η (fun (j : η) => Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (fun (i : η) => Finsupp.addCommMonoid.{u3, u4} (ιs i) M _inst_11)) (Pi.module.{u1, max u4 u3, u2} η (fun (j : η) => Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) R _inst_1 (fun (i : η) => Finsupp.addCommMonoid.{u3, u4} (ιs i) M _inst_11) (fun (i : η) => Finsupp.module.{u3, u4, u2} (ιs i) M R _inst_1 _inst_11 _inst_12))) (Module.toDistribMulAction.{u2, max (max u3 u4) u1} R (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) _inst_1 (Finsupp.addCommMonoid.{max u1 u3, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M _inst_11) (Finsupp.module.{max u1 u3, u4, u2} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M R _inst_1 _inst_11 _inst_12)) (SemilinearMapClass.distribMulActionHomClass.{u2, max (max u3 u4) u1, max (max u3 u4) u1, max (max u3 u4) u1} R (forall (j : η), Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (LinearEquiv.{u2, u2, max (max u3 u4) u1, max (max u3 u4) u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (forall (j : η), Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (Pi.addCommMonoid.{u1, max u4 u3} η (fun (j : η) => Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (fun (i : η) => Finsupp.addCommMonoid.{u3, u4} (ιs i) M _inst_11)) (Finsupp.addCommMonoid.{max u1 u3, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M _inst_11) (Pi.module.{u1, max u4 u3, u2} η (fun (j : η) => Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) R _inst_1 (fun (i : η) => Finsupp.addCommMonoid.{u3, u4} (ιs i) M _inst_11) (fun (i : η) => Finsupp.module.{u3, u4, u2} (ιs i) M R _inst_1 _inst_11 _inst_12)) (Finsupp.module.{max u1 u3, u4, u2} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M R _inst_1 _inst_11 _inst_12)) _inst_1 (Pi.addCommMonoid.{u1, max u4 u3} η (fun (j : η) => Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (fun (i : η) => Finsupp.addCommMonoid.{u3, u4} (ιs i) M _inst_11)) (Finsupp.addCommMonoid.{max u1 u3, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M _inst_11) (Pi.module.{u1, max u4 u3, u2} η (fun (j : η) => Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) R _inst_1 (fun (i : η) => Finsupp.addCommMonoid.{u3, u4} (ιs i) M _inst_11) (fun (i : η) => Finsupp.module.{u3, u4, u2} (ιs i) M R _inst_1 _inst_11 _inst_12)) (Finsupp.module.{max u1 u3, u4, u2} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M R _inst_1 _inst_11 _inst_12) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max (max u3 u4) u1, max (max u3 u4) u1, max (max u3 u4) u1} R R (forall (j : η), Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (LinearEquiv.{u2, u2, max (max u3 u4) u1, max (max u3 u4) u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} 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(_x : ιs (Sigma.fst.{u1, u3} η (fun (j : η) => ιs j) ji)) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ιs (Sigma.fst.{u1, u3} η (fun (j : η) => ιs j) ji)) => M) _x) (Finsupp.funLike.{u3, u4} (ιs (Sigma.fst.{u1, u3} η (fun (j : η) => ιs j) ji)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (f (Sigma.fst.{u1, u3} η (fun (j : η) => ιs j) ji)) (Sigma.snd.{u1, u3} η (fun (j : η) => ιs j) ji))
Case conversion may be inaccurate. Consider using '#align finsupp.sigma_finsupp_lequiv_pi_finsupp_symm_apply Finsupp.sigmaFinsuppLEquivPiFinsupp_symm_applyₓ'. -/
@[simp]
theorem sigmaFinsuppLEquivPiFinsupp_symm_apply {M : Type _} {ιs : η → Type _} [AddCommMonoid M]
@@ -1727,7 +1727,7 @@ noncomputable def finsuppProdLEquiv {α β : Type _} (R : Type _) {M : Type _} [
lean 3 declaration is
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(AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_10)))) (Finsupp.addCommMonoid.{u2, u4} β M _inst_10)) (Finsupp.module.{max u1 u2, u4, u3} (Prod.{u1, u2} α β) M R _inst_9 _inst_10 _inst_11) (Finsupp.module.{u1, max u2 u4, u3} α (Finsupp.{u2, u4} β M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_10)))) R _inst_9 (Finsupp.addCommMonoid.{u2, u4} β M _inst_10) (Finsupp.module.{u2, u4, u3} β M R _inst_9 _inst_10 _inst_11))) (fun (_x : LinearEquiv.{u3, u3, max (max u1 u2) u4, max u1 u2 u4} R R _inst_9 _inst_9 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_9)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_9)) (RingHomInvPair.ids.{u3} R _inst_9) (RingHomInvPair.ids.{u3} R _inst_9) (Finsupp.{max u1 u2, u4} (Prod.{u1, u2} α β) M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_10)))) (Finsupp.{u1, max u2 u4} α (Finsupp.{u2, u4} β M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_10)))) (Finsupp.zero.{u2, u4} β M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_10))))) (Finsupp.addCommMonoid.{max u1 u2, u4} (Prod.{u1, u2} α β) M _inst_10) (Finsupp.addCommMonoid.{u1, max u2 u4} α (Finsupp.{u2, u4} β M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_10)))) (Finsupp.addCommMonoid.{u2, u4} β M _inst_10)) (Finsupp.module.{max u1 u2, u4, u3} (Prod.{u1, u2} α β) M R _inst_9 _inst_10 _inst_11) (Finsupp.module.{u1, max u2 u4, u3} α (Finsupp.{u2, u4} β M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_10)))) R _inst_9 (Finsupp.addCommMonoid.{u2, u4} β M _inst_10) (Finsupp.module.{u2, u4, u3} β M R _inst_9 _inst_10 _inst_11))) => (Finsupp.{max u1 u2, u4} (Prod.{u1, u2} α β) M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_10)))) -> (Finsupp.{u1, max u2 u4} α (Finsupp.{u2, u4} β M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_10)))) (Finsupp.zero.{u2, u4} β M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_10)))))) (LinearEquiv.hasCoeToFun.{u3, u3, max (max u1 u2) u4, max u1 u2 u4} R R (Finsupp.{max u1 u2, u4} (Prod.{u1, u2} α β) M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_10)))) (Finsupp.{u1, max u2 u4} α (Finsupp.{u2, u4} β M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_10)))) (Finsupp.zero.{u2, u4} β M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_10))))) _inst_9 _inst_9 (Finsupp.addCommMonoid.{max u1 u2, u4} (Prod.{u1, u2} α β) M _inst_10) (Finsupp.addCommMonoid.{u1, max u2 u4} α (Finsupp.{u2, u4} β M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_10)))) (Finsupp.addCommMonoid.{u2, u4} β M _inst_10)) (Finsupp.module.{max u1 u2, u4, u3} (Prod.{u1, u2} α β) M R _inst_9 _inst_10 _inst_11) (Finsupp.module.{u1, max u2 u4, u3} α (Finsupp.{u2, u4} β M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_10)))) R _inst_9 (Finsupp.addCommMonoid.{u2, u4} β M _inst_10) (Finsupp.module.{u2, u4, u3} β M R _inst_9 _inst_10 _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_9)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_9)) (RingHomInvPair.ids.{u3} R _inst_9) (RingHomInvPair.ids.{u3} R _inst_9)) (Finsupp.finsuppProdLEquiv.{u1, u2, u3, u4} α β R M _inst_9 _inst_10 _inst_11) f) x) y) (coeFn.{max (succ (max u1 u2)) (succ u4), max (succ (max u1 u2)) (succ u4)} 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but is expected to have type
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+ forall {α : Type.{u4}} {β : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_9 : Semiring.{u2} R] [_inst_10 : AddCommMonoid.{u1} M] [_inst_11 : Module.{u2, u1} R M _inst_9 _inst_10] (f : Finsupp.{max u3 u4, u1} (Prod.{u4, u3} α β) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (x : α) (y : β), Eq.{succ u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : β) => M) y) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) β (fun (_x : β) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : β) => M) _x) (Finsupp.funLike.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (FunLike.coe.{max (succ u4) (succ (max u3 u1)), succ u4, succ (max u3 u1)} (Finsupp.{u4, max u3 u1} α (Finsupp.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (Finsupp.zero.{u3, u1} β M (AddMonoid.toZero.{u1} M 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(AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (Finsupp.{u4, max u1 u3} α (Finsupp.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (Finsupp.zero.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_9)) (AddCommMonoid.toAddMonoid.{max (max u1 u3) u4} (Finsupp.{max u3 u4, u1} (Prod.{u4, u3} α β) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (Finsupp.addCommMonoid.{max u4 u3, u1} (Prod.{u4, u3} α β) M _inst_10)) (AddCommMonoid.toAddMonoid.{max (max u1 u3) u4} (Finsupp.{u4, max u1 u3} α (Finsupp.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (Finsupp.zero.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10)))) (Finsupp.addCommMonoid.{u4, max u3 u1} α (Finsupp.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (Finsupp.addCommMonoid.{u3, u1} β M _inst_10))) (Module.toDistribMulAction.{u2, max (max u1 u3) u4} R (Finsupp.{max u3 u4, u1} (Prod.{u4, u3} α β) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) _inst_9 (Finsupp.addCommMonoid.{max u4 u3, u1} (Prod.{u4, u3} α β) M _inst_10) (Finsupp.module.{max u4 u3, u1, u2} (Prod.{u4, u3} α β) M R _inst_9 _inst_10 _inst_11)) (Module.toDistribMulAction.{u2, max (max u1 u3) u4} R (Finsupp.{u4, max u1 u3} α (Finsupp.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (Finsupp.zero.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10)))) _inst_9 (Finsupp.addCommMonoid.{u4, max u3 u1} α (Finsupp.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (Finsupp.addCommMonoid.{u3, u1} β M _inst_10)) (Finsupp.module.{u4, max u3 u1, u2} α (Finsupp.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) R _inst_9 (Finsupp.addCommMonoid.{u3, u1} β M _inst_10) (Finsupp.module.{u3, u1, u2} β M R _inst_9 _inst_10 _inst_11))) (SemilinearMapClass.distribMulActionHomClass.{u2, max (max u1 u3) u4, max (max u1 u3) u4, max (max u1 u3) u4} R (Finsupp.{max u3 u4, u1} (Prod.{u4, u3} α β) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (Finsupp.{u4, max u1 u3} α (Finsupp.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (Finsupp.zero.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10)))) (LinearEquiv.{u2, u2, max u1 u3 u4, max (max u1 u3) u4} R R _inst_9 _inst_9 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_9)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_9)) (RingHomInvPair.ids.{u2} R _inst_9) (RingHomInvPair.ids.{u2} R _inst_9) (Finsupp.{max u3 u4, u1} (Prod.{u4, u3} α β) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (Finsupp.{u4, max u1 u3} α (Finsupp.{u3, u1} 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Case conversion may be inaccurate. Consider using '#align finsupp.finsupp_prod_lequiv_apply Finsupp.finsuppProdLEquiv_applyₓ'. -/
@[simp]
theorem finsuppProdLEquiv_apply {α β R M : Type _} [Semiring R] [AddCommMonoid M] [Module R M]
@@ -1739,7 +1739,7 @@ theorem finsuppProdLEquiv_apply {α β R M : Type _} [Semiring R] [AddCommMonoid
lean 3 declaration is
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_inst_11)) (Finsupp.module.{max u4 u3, u1, u2} (Prod.{u4, u3} α β) M R _inst_9 _inst_10 _inst_11) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max (max u1 u3) u4, max (max u1 u3) u4, max (max u1 u3) u4} R R (Finsupp.{u4, max u1 u3} α (Finsupp.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (Finsupp.zero.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10)))) (Finsupp.{max u3 u4, u1} (Prod.{u4, u3} α β) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (LinearEquiv.{u2, u2, max (max u1 u3) u4, max (max u1 u3) u4} R R _inst_9 _inst_9 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_9)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_9)) (RingHomInvPair.ids.{u2} R _inst_9) (RingHomInvPair.ids.{u2} R _inst_9) (Finsupp.{u4, max u1 u3} α (Finsupp.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (Finsupp.zero.{u3, u1} β M 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+ forall {α : Type.{u4}} {β : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_9 : Semiring.{u2} R] [_inst_10 : AddCommMonoid.{u1} M] [_inst_11 : Module.{u2, u1} R M _inst_9 _inst_10] (f : Finsupp.{u4, max u1 u3} α (Finsupp.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (Finsupp.zero.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10)))) (xy : Prod.{u4, u3} α β), Eq.{succ u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Prod.{u4, u3} α β) => M) xy) (FunLike.coe.{max (succ (max u4 u3)) (succ u1), succ (max u4 u3), succ u1} (Finsupp.{max u4 u3, u1} (Prod.{u4, u3} α β) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (Prod.{u4, u3} α β) (fun (_x : Prod.{u4, u3} α β) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Prod.{u4, u3} α β) => M) _x) (Finsupp.funLike.{max u4 u3, u1} (Prod.{u4, u3} α β) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (FunLike.coe.{max (max 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(Module.toDistribMulAction.{u2, max (max u1 u3) u4} R (Finsupp.{max u3 u4, u1} (Prod.{u4, u3} α β) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) _inst_9 (Finsupp.addCommMonoid.{max u4 u3, u1} (Prod.{u4, u3} α β) M _inst_10) (Finsupp.module.{max u4 u3, u1, u2} (Prod.{u4, u3} α β) M R _inst_9 _inst_10 _inst_11))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u3) u4, u2, max (max u1 u3) u4, max (max u1 u3) u4} (LinearEquiv.{u2, u2, max (max u1 u3) u4, max (max u1 u3) u4} R R _inst_9 _inst_9 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_9)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_9)) (RingHomInvPair.ids.{u2} R _inst_9) (RingHomInvPair.ids.{u2} R _inst_9) (Finsupp.{u4, max u1 u3} α (Finsupp.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (Finsupp.zero.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10)))) (Finsupp.{max u3 u4, u1} (Prod.{u4, u3} α β) M 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(MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_9)) (AddCommMonoid.toAddMonoid.{max (max u1 u3) u4} (Finsupp.{u4, max u1 u3} α (Finsupp.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (Finsupp.zero.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10)))) (Finsupp.addCommMonoid.{u4, max u3 u1} α (Finsupp.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (Finsupp.addCommMonoid.{u3, u1} β M _inst_10))) (AddCommMonoid.toAddMonoid.{max (max u1 u3) u4} (Finsupp.{max u3 u4, u1} (Prod.{u4, u3} α β) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (Finsupp.addCommMonoid.{max u4 u3, u1} (Prod.{u4, u3} α β) M _inst_10)) (Module.toDistribMulAction.{u2, max (max u1 u3) u4} R (Finsupp.{u4, max u1 u3} α (Finsupp.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (Finsupp.zero.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10)))) _inst_9 (Finsupp.addCommMonoid.{u4, max u3 u1} α (Finsupp.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (Finsupp.addCommMonoid.{u3, u1} β M _inst_10)) (Finsupp.module.{u4, max u3 u1, u2} α (Finsupp.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) R _inst_9 (Finsupp.addCommMonoid.{u3, u1} β M _inst_10) (Finsupp.module.{u3, u1, u2} β M R _inst_9 _inst_10 _inst_11))) (Module.toDistribMulAction.{u2, max (max u1 u3) u4} R (Finsupp.{max u3 u4, u1} (Prod.{u4, u3} α β) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) _inst_9 (Finsupp.addCommMonoid.{max u4 u3, u1} (Prod.{u4, u3} α β) M _inst_10) (Finsupp.module.{max u4 u3, u1, u2} (Prod.{u4, u3} α β) M R _inst_9 _inst_10 _inst_11)) (SemilinearMapClass.distribMulActionHomClass.{u2, max (max u1 u3) u4, max (max u1 u3) u4, max (max u1 u3) u4} R (Finsupp.{u4, max u1 u3} α (Finsupp.{u3, u1} β M 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_inst_11)) (Finsupp.module.{max u4 u3, u1, u2} (Prod.{u4, u3} α β) M R _inst_9 _inst_10 _inst_11) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max (max u1 u3) u4, max (max u1 u3) u4, max (max u1 u3) u4} R R (Finsupp.{u4, max u1 u3} α (Finsupp.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (Finsupp.zero.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10)))) (Finsupp.{max u3 u4, u1} (Prod.{u4, u3} α β) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (LinearEquiv.{u2, u2, max (max u1 u3) u4, max (max u1 u3) u4} R R _inst_9 _inst_9 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_9)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_9)) (RingHomInvPair.ids.{u2} R _inst_9) (RingHomInvPair.ids.{u2} R _inst_9) (Finsupp.{u4, max u1 u3} α (Finsupp.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (Finsupp.zero.{u3, u1} β M 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_inst_9)) (RingHomInvPair.ids.{u2} R _inst_9) (RingHomInvPair.ids.{u2} R _inst_9) (Finsupp.finsuppProdLEquiv.{u4, u3, u2, u1} α β R M _inst_9 _inst_10 _inst_11)) f) xy) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) β (fun (_x : β) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : β) => M) _x) (Finsupp.funLike.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (FunLike.coe.{max (succ u4) (succ (max u3 u1)), succ u4, succ (max u3 u1)} (Finsupp.{u4, max u3 u1} α (Finsupp.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (Finsupp.zero.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10)))) α (fun (_x : α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => Finsupp.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) _x) (Finsupp.funLike.{u4, max u3 u1} α 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Case conversion may be inaccurate. Consider using '#align finsupp.finsupp_prod_lequiv_symm_apply Finsupp.finsuppProdLEquiv_symm_applyₓ'. -/
@[simp]
theorem finsuppProdLEquiv_symm_apply {α β R M : Type _} [Semiring R] [AddCommMonoid M] [Module R M]
@@ -1792,7 +1792,7 @@ variable {S}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] {S : Type.{u4}} [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (f : α -> R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R 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(Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) f) (Finset.sum.{u2, u1} M α _inst_3 (Finset.univ.{u1} α _inst_1) (fun (i : α) => SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (f i) (v i)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (f : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : α -> R) => M) f) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) v) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearMap.{u1, u1, max u3 u4, max u4 u3 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => 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(α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) f) (Finset.sum.{u4, u3} M α _inst_3 (Finset.univ.{u3} α _inst_1) (fun (i : α) => HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) (f i) (v i)))
+ forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (f : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : α -> R) => M) f) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearMap.{u1, u1, max u3 u4, max u4 u3 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u3, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) f) (Finset.sum.{u4, u3} M α _inst_3 (Finset.univ.{u3} α _inst_1) (fun (i : α) => HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) (f i) (v i)))
Case conversion may be inaccurate. Consider using '#align fintype.total_apply Fintype.total_applyₓ'. -/
theorem Fintype.total_apply (f) : Fintype.total R S v f = ∑ i, f i • v i :=
rfl
@@ -1802,7 +1802,7 @@ theorem Fintype.total_apply (f) : Fintype.total R S v f = ∑ i, f i • v i :=
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] {S : Type.{u4}} [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (i : α) (r : R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R 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(Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) (Pi.single.{u1, u3} α (fun (ᾰ : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u1} α a b)) (fun (i : α) => MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) i r)) (SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) r (v i))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (i : α) (r : R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : α -> R) => M) (Pi.single.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} 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(AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) r (v i))
+ forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (i : α) (r : R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : α -> R) => M) (Pi.single.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} 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(i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) (Pi.single.{u3, u2} α (fun (ᾰ : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) r (v i))
Case conversion may be inaccurate. Consider using '#align fintype.total_apply_single Fintype.total_apply_singleₓ'. -/
@[simp]
theorem Fintype.total_apply_single (i : α) (r : R) :
@@ -1818,7 +1818,7 @@ variable (S)
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] (S : Type.{u4}) [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (x : α -> R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R 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u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Finsupp.total.{u1, u2, u3} α M R _inst_2 _inst_3 _inst_4 v) (coeFn.{succ (max u1 u3), succ (max u1 u3)} (LinearEquiv.{u3, u3, max u1 u3, max u1 u3} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHomInvPair.ids.{u3} R _inst_2) (RingHomInvPair.ids.{u3} R _inst_2) (α -> R) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R 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(Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) x)
but is expected to have type
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(MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (x : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) => M) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (α -> R) (fun (a : α -> R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> R) => Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) a) (SMulHomClass.toFunLike.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (α -> R) (AddMonoid.toZero.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (α -> R) (AddMonoid.toAddZeroClass.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (α -> R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u3 u2, max u3 u2, max u3 u2} R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u3 u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α 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(AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 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(fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearMap.{u1, u1, max u3 u4, max u4 u3 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun 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(Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) x)
+ forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (x : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) => M) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (α -> R) (fun (a : α -> R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : α -> R) => Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) a) (SMulHomClass.toFunLike.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (α -> R) (AddMonoid.toZero.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (α -> R) (AddMonoid.toAddZeroClass.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (α -> R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u3 u2, max u3 u2, max u3 u2} R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u3 u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α 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(AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 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R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u3 u2, max u3 u2, max u3 u2} R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} 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Case conversion may be inaccurate. Consider using '#align finsupp.total_eq_fintype_total_apply Finsupp.total_eq_fintype_total_applyₓ'. -/
theorem Finsupp.total_eq_fintype_total_apply (x : α → R) :
Finsupp.total α M R v ((Finsupp.linearEquivFunOnFinite R R α).symm x) = Fintype.total R S v x :=
@@ -1834,7 +1834,7 @@ theorem Finsupp.total_eq_fintype_total_apply (x : α → R) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] (S : Type.{u4}) [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (LinearMap.comp.{u3, u3, u3, max u1 u3, max u1 u3, u2} R R R (α -> R) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))) M _inst_2 _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHomCompTriple.right_ids.{u3, u3} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Finsupp.total.{u1, u2, u3} α M R _inst_2 _inst_3 _inst_4 v) (LinearEquiv.toLinearMap.{u3, u3, max u1 u3, max u1 u3} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHomInvPair.ids.{u3} R _inst_2) (RingHomInvPair.ids.{u3} R _inst_2) (α -> R) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))))) (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) (LinearEquiv.symm.{u3, u3, max u1 u3, max u1 u3} R R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))))) (α -> R) _inst_2 _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHomInvPair.ids.{u3} R _inst_2) (RingHomInvPair.ids.{u3} R _inst_2) (Finsupp.linearEquivFunOnFinite.{u3, u3, u1} R R α (Finite.of_fintype.{u1} α _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) _inst_2 (Semiring.toModule.{u3} R _inst_2))))) (coeFn.{max (succ (max u1 u2)) (succ (max (max u1 u3) u2)), max (succ (max u1 u2)) (succ (max (max u1 u3) u2))} (LinearMap.{u4, u4, max u1 u2, max (max u1 u3) u2} S S _inst_5 _inst_5 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4)) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, max (max u1 u3) u2} S S (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)
but is expected to have type
- forall {α : Type.{u4}} {M : Type.{u3}} (R : Type.{u2}) [_inst_1 : Fintype.{u4} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u3} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u3} R S M (SMulZeroClass.toSMul.{u2, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u2, u3} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u3} S M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u1, u3} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (LinearMap.comp.{u2, u2, u2, max u4 u2, max u4 u2, u3} R R R (α -> R) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) M _inst_2 _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomCompTriple.ids.{u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Finsupp.total.{u4, u3, u2} α M R _inst_2 _inst_3 _inst_4 v) (LinearEquiv.toLinearMap.{u2, u2, max u4 u2, max u4 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u4, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (LinearEquiv.symm.{u2, u2, max u4 u2, max u4 u2} R R (Finsupp.{u4, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (α -> R) _inst_2 _inst_2 (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (Finsupp.linearEquivFunOnFinite.{u2, u2, u4} R R α (Finite.of_fintype.{u4} α _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) _inst_2 (Semiring.toModule.{u2} R _inst_2))))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), max (max (succ u2) (succ u3)) (succ u4)} (LinearMap.{u1, u1, max u4 u3, max u3 u4 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u4, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u4 u2, u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u4, u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u4 u2, u3} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : α -> M) => LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u4, max (max u2 u3) u4} S S (α -> M) (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u4, u3} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u4 u2, u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u4, u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u4 u2, u3} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u4, u3, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)
+ forall {α : Type.{u4}} {M : Type.{u3}} (R : Type.{u2}) [_inst_1 : Fintype.{u4} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u3} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u3} R S M (SMulZeroClass.toSMul.{u2, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u2, u3} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u3} S M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u1, u3} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (LinearMap.comp.{u2, u2, u2, max u4 u2, max u4 u2, u3} R R R (α -> R) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) M _inst_2 _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomCompTriple.ids.{u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Finsupp.total.{u4, u3, u2} α M R _inst_2 _inst_3 _inst_4 v) (LinearEquiv.toLinearMap.{u2, u2, max u4 u2, max u4 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u4, u2} α R (AddMonoid.toZero.{u2} R 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_inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u4, u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u4 u2, u3} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u4, u3, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)
Case conversion may be inaccurate. Consider using '#align finsupp.total_eq_fintype_total Finsupp.total_eq_fintype_totalₓ'. -/
theorem Finsupp.total_eq_fintype_total :
(Finsupp.total α M R v).comp (Finsupp.linearEquivFunOnFinite R R α).symm.toLinearMap =
@@ -1848,7 +1848,7 @@ variable {S}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] {S : Type.{u4}} [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{succ u2} (Submodule.{u3, u2} R M _inst_2 _inst_3 _inst_4) (LinearMap.range.{u3, u3, max u1 u3, u2, max (max u1 u3) u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (LinearMap.semilinearMapClass.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (RingHomSurjective.ids.{u3} R _inst_2) (coeFn.{max (succ (max u1 u2)) (succ (max (max u1 u3) u2)), max (succ (max u1 u2)) (succ (max (max u1 u3) u2))} (LinearMap.{u4, u4, max u1 u2, max (max u1 u3) u2} S S _inst_5 _inst_5 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) (fun (_x : LinearMap.{u4, u4, max u1 u2, max (max u1 u3) u2} S S _inst_5 _inst_5 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) => (α -> M) -> (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4)) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, max (max u1 u3) u2} S S (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)) (Submodule.span.{u3, u2} R M _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u1} M α v))
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u4}} (R : Type.{u3}) [_inst_1 : Fintype.{u2} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u3, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u1, u4} R S M (SMulZeroClass.toSMul.{u3, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u4} R M (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u4} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u3, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{succ u4} (Submodule.{u3, u4} R M _inst_2 _inst_3 _inst_4) (LinearMap.range.{u3, u3, max u2 u3, u4, max (max u2 u4) u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : α -> M) => LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) v) (LinearMap.semilinearMapClass.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (RingHomSurjective.ids.{u3} R _inst_2) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearMap.{u1, u1, max u2 u4, max u4 u2 u3} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u2, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => 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α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u2 u3, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u2, u4, u3, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)) (Submodule.span.{u3, u4} R M _inst_2 _inst_3 _inst_4 (Set.range.{u4, succ u2} M α v))
+ forall {α : Type.{u2}} {M : Type.{u4}} (R : Type.{u3}) [_inst_1 : Fintype.{u2} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u3, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u1, u4} R S M (SMulZeroClass.toSMul.{u3, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u4} R M (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u4} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u3, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{succ u4} (Submodule.{u3, u4} R M _inst_2 _inst_3 _inst_4) (LinearMap.range.{u3, u3, max u2 u3, u4, max (max u2 u4) u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : α -> M) => LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) v) (LinearMap.semilinearMapClass.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (RingHomSurjective.ids.{u3} R _inst_2) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearMap.{u1, u1, max u2 u4, max u4 u2 u3} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u2, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : α -> M) => LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u2, max (max u3 u4) u2} S S (α -> M) (LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u2, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.module.{u2, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u2 u3, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u2, u4, u3, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)) (Submodule.span.{u3, u4} R M _inst_2 _inst_3 _inst_4 (Set.range.{u4, succ u2} M α v))
Case conversion may be inaccurate. Consider using '#align fintype.range_total Fintype.range_totalₓ'. -/
@[simp]
theorem Fintype.range_total : (Fintype.total R S v).range = Submodule.span R (Set.range v) := by
@@ -1920,7 +1920,7 @@ irreducible_def Span.repr (w : Set M) (x : span R w) : w →₀ R :=
lean 3 declaration is
forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {w : Set.{u2} M} (x : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w)), Eq.{succ u2} M (coeFn.{max (succ (max u2 u1)) (succ u2), max (succ (max u2 u1)) (succ u2)} (LinearMap.{u1, u1, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) w) R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (Finsupp.addCommMonoid.{u2, u1} 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(Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w)) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w)) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w)) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w)) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w)))))) x)
but is expected to have type
- forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {w : Set.{u2} M} (x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) (Span.repr.{u1, u2} R M _inst_1 _inst_2 _inst_3 w x)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} (Set.Elem.{u2} M w) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} (Set.Elem.{u2} M w) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) (Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u2} R R (Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} (Set.Elem.{u2} M w) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} (Set.Elem.{u2} M w) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} (Set.Elem.{u2} M w) M R _inst_1 _inst_2 _inst_3 (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x w))) (Span.repr.{u1, u2} R M _inst_1 _inst_2 _inst_3 w x)) (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w))) x)
+ forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {w : Set.{u2} M} (x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) (Span.repr.{u1, u2} R M _inst_1 _inst_2 _inst_3 w x)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} (Set.Elem.{u2} M w) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} (Set.Elem.{u2} M w) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) (Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u2} R R (Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} (Set.Elem.{u2} M w) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} (Set.Elem.{u2} M w) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} (Set.Elem.{u2} M w) M R _inst_1 _inst_2 _inst_3 (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x w))) (Span.repr.{u1, u2} R M _inst_1 _inst_2 _inst_3 w x)) (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w))) x)
Case conversion may be inaccurate. Consider using '#align span.finsupp_total_repr Span.finsupp_total_reprₓ'. -/
@[simp]
theorem Span.finsupp_total_repr {w : Set M} (x : span R w) :
@@ -1947,7 +1947,7 @@ protected theorem Submodule.finsupp_sum_mem {ι β : Type _} [Zero β] (S : Subm
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_4] (f : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M N _inst_2 _inst_4 _inst_3 _inst_5) {ι : Type.{u4}} {g : ι -> M} (l : Finsupp.{u4, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))), Eq.{succ u3} N (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M N _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M N _inst_2 _inst_4 _inst_3 _inst_5) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M N _inst_1 _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u4, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (Finsupp.addCommMonoid.{u4, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u4, u1, u1} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u4, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (Finsupp.addCommMonoid.{u4, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u4, u1, u1} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) => (Finsupp.{u4, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} R R (Finsupp.{u4, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u4, u1, u1} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u4, u2, u1} ι M R _inst_1 _inst_2 _inst_3 g) l)) (coeFn.{max (succ (max u4 u1)) (succ u3), max (succ (max u4 u1)) (succ u3)} (LinearMap.{u1, u1, max u4 u1, 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) N (Finsupp.addCommMonoid.{u4, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_4 (Finsupp.module.{u4, u1, u1} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_5) => (Finsupp.{u4, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) -> N) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u3} R R (Finsupp.{u4, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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(x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u4 u1, u3} R R (Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u4, u4} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Finsupp.total.{u1, u3, u4} ι M R _inst_1 _inst_2 _inst_3 g) l)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u1), max (succ u4) (succ u1), succ u2} (LinearMap.{u4, u4, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) N (Finsupp.addCommMonoid.{u1, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_4 (Finsupp.module.{u1, u4, u4} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_5) (Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) (fun (_x : Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u4 u1, u2} R R (Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_4 (Finsupp.module.{u1, u4, u4} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Finsupp.total.{u1, u2, u4} ι N R _inst_1 _inst_4 _inst_5 (Function.comp.{succ u1, succ u3, succ u2} ι M N (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (LinearMap.{u4, u4, u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_2 _inst_4 _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, u2} R R M N _inst_1 _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) f) g)) l)
Case conversion may be inaccurate. Consider using '#align linear_map.map_finsupp_total LinearMap.map_finsupp_totalₓ'. -/
theorem LinearMap.map_finsupp_total (f : M →ₗ[R] N) {ι : Type _} {g : ι → M} (l : ι →₀ R) :
f (Finsupp.total ι M R g l) = Finsupp.total ι N R (f ∘ g) l := by
@@ -2043,7 +2043,7 @@ open Finsupp Function
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_1 _inst_1 _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3)
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} (f : LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u1) (succ u3)} M (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u3} R R M (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _inst_1 _inst_1 _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} (f : LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u1) (succ u3)} M (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u3} R R M (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _inst_1 _inst_1 _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3)
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_finsupp_surjective LinearMap.splittingOfFinsuppSurjectiveₓ'. -/
-- See also `linear_map.splitting_of_fun_on_fintype_surjective`
/-- A surjective linear map to finitely supported functions has a splitting. -/
@@ -2055,7 +2055,7 @@ def splittingOfFinsuppSurjective (f : M →ₗ[R] α →₀ R) (s : Surjective f
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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but is expected to have type
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (LinearMap.comp.{u3, u3, u3, max u3 u1, u2, max u3 u1} R R R (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} 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+ forall {R : Type.{u3}} {M : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u3, u2} R M _inst_1 _inst_2] {α : Type.{u1}} (f : LinearMap.{u3, u3, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (FunLike.coe.{max 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(MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_1 _inst_1 _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)), Eq.{max (succ u3) (succ u1)} (LinearMap.{u3, u3, max u3 u1, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (LinearMap.comp.{u3, u3, u3, max u3 u1, u2, max u3 u1} R R R (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomCompTriple.ids.{u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f (LinearMap.splittingOfFinsuppSurjective.{u3, u2, u1} R M _inst_1 _inst_2 _inst_3 α f s)) (LinearMap.id.{u3, max u3 u1} R (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)))
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_finsupp_surjective_splits LinearMap.splittingOfFinsuppSurjective_splitsₓ'. -/
theorem splittingOfFinsuppSurjective_splits (f : M →ₗ[R] α →₀ R) (s : Surjective f) :
f.comp (splittingOfFinsuppSurjective f s) = LinearMap.id :=
@@ -2072,7 +2072,7 @@ theorem splittingOfFinsuppSurjective_splits (f : M →ₗ[R] α →₀ R) (s : S
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M 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_inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_1 _inst_1 _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Function.LeftInverse.{max (succ u3) (succ u1), succ u2} (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 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but is expected to have type
- forall {R : Type.{u3}} {M : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u3, u2} R M _inst_1 _inst_2] {α : Type.{u1}} (f : LinearMap.{u3, u3, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (FunLike.coe.{max 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+ forall {R : Type.{u3}} {M : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u3, u2} R M _inst_1 _inst_2] {α : Type.{u1}} (f : LinearMap.{u3, u3, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (FunLike.coe.{max 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.splittingOfFinsuppSurjective.{u3, u2, u1} R M _inst_1 _inst_2 _inst_3 α f s))
Case conversion may be inaccurate. Consider using '#align linear_map.left_inverse_splitting_of_finsupp_surjective LinearMap.leftInverse_splittingOfFinsuppSurjectiveₓ'. -/
theorem leftInverse_splittingOfFinsuppSurjective (f : M →ₗ[R] α →₀ R) (s : Surjective f) :
LeftInverse f (splittingOfFinsuppSurjective f s) := fun g =>
@@ -2083,7 +2083,7 @@ theorem leftInverse_splittingOfFinsuppSurjective (f : M →ₗ[R] α →₀ R) (
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M 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(Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_1 _inst_1 _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Function.Injective.{max (succ u3) (succ u1), succ u2} (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R 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(MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.splittingOfFinsuppSurjective.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 α f s))
but is expected to have type
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+ forall {R : Type.{u3}} {M : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u3, u2} R M _inst_1 _inst_2] {α : Type.{u1}} (f : LinearMap.{u3, u3, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u2, max (succ u3) (succ u1)} (LinearMap.{u3, u3, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, max u3 u1} R R M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_1 _inst_1 _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)), Function.Injective.{max (succ u3) (succ u1), succ u2} (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u1), succ u2} (LinearMap.{u3, u3, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_3) (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (fun (_x : Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u1, u2} R R (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.splittingOfFinsuppSurjective.{u3, u2, u1} R M _inst_1 _inst_2 _inst_3 α f s))
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_finsupp_surjective_injective LinearMap.splittingOfFinsuppSurjective_injectiveₓ'. -/
theorem splittingOfFinsuppSurjective_injective (f : M →ₗ[R] α →₀ R) (s : Surjective f) :
Injective (splittingOfFinsuppSurjective f s) :=
@@ -2094,7 +2094,7 @@ theorem splittingOfFinsuppSurjective_injective (f : M →ₗ[R] α →₀ R) (s
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3)
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u1) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) _inst_3)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u1) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) _inst_3)
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective LinearMap.splittingOfFunOnFintypeSurjectiveₓ'. -/
-- See also `linear_map.splitting_of_finsupp_surjective`
/-- A surjective linear map to functions on a finite type has a splitting. -/
@@ -2108,7 +2108,7 @@ def splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R) (s
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Eq.{succ (max u3 u1)} (LinearMap.{u1, u1, max u3 u1, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (LinearMap.comp.{u1, u1, u1, max u3 u1, u2, max u3 u1} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomCompTriple.right_ids.{u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u1, max u3 u1} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17208 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17208 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17208 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17208 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Eq.{max (succ u2) (succ u3)} (LinearMap.{u2, u2, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17208 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.comp.{u2, u2, u2, max u2 u3, u1, max u2 u3} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17208 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u2, max u2 u3} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17208 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17208 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17208 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17208 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Eq.{max (succ u2) (succ u3)} (LinearMap.{u2, u2, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17208 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.comp.{u2, u2, u2, max u2 u3, u1, max u2 u3} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17208 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u2, max u2 u3} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)))
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective_splits LinearMap.splittingOfFunOnFintypeSurjective_splitsₓ'. -/
theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : f.comp (splittingOfFunOnFintypeSurjective f s) = LinearMap.id :=
@@ -2124,7 +2124,7 @@ theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R]
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Function.LeftInverse.{max (succ u3) (succ u1), succ u2} (α -> R) M (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f) (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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but is expected to have type
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => 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Case conversion may be inaccurate. Consider using '#align linear_map.left_inverse_splitting_of_fun_on_fintype_surjective LinearMap.leftInverse_splittingOfFunOnFintypeSurjectiveₓ'. -/
theorem leftInverse_splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : LeftInverse f (splittingOfFunOnFintypeSurjective f s) := fun g =>
@@ -2135,7 +2135,7 @@ theorem leftInverse_splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Function.Injective.{max (succ u3) (succ u1), succ u2} (α -> R) M (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) (fun (_x : LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) => (α -> R) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, u2} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17399 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17399 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17399 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17399 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Function.Injective.{max (succ u2) (succ u3), succ u1} (α -> R) M (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17399 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17399 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17399 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17399 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Function.Injective.{max (succ u2) (succ u3), succ u1} (α -> R) M (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective_injective LinearMap.splittingOfFunOnFintypeSurjective_injectiveₓ'. -/
theorem splittingOfFunOnFintypeSurjective_injective [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : Injective (splittingOfFunOnFintypeSurjective f s) :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4
@@ -1095,7 +1095,7 @@ theorem total_mapDomain (f : α → α') (l : α →₀ R) :
lean 3 declaration is
forall {α : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] {α' : Type.{u3}} {M' : Type.{u4}} [_inst_9 : AddCommMonoid.{u4} M'] [_inst_10 : Module.{u2, u4} R M' _inst_1 _inst_9] {v' : α' -> M'} (f : Equiv.{succ u1, succ u3} α α') (l : Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))), Eq.{succ u4} M' (coeFn.{max (succ (max u3 u2)) (succ u4), max (succ (max u3 u2)) (succ u4)} (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) (fun (_x : LinearMap.{u2, u2, max u3 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) => (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M') (LinearMap.hasCoeToFun.{u2, u2, max u3 u2, u4} R R (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R 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but is expected to have type
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+ forall {α : Type.{u4}} (R : Type.{u2}) {_inst_1 : Type.{u3}} {α' : Type.{u1}} [M' : Semiring.{u2} R] [_inst_9 : AddCommMonoid.{u1} α'] [_inst_10 : Module.{u2, u1} R α' M' _inst_9] {v' : _inst_1 -> α'} (f : Equiv.{succ u4, succ u3} α _inst_1) (l : Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) => α') (Finsupp.equivMapDomain.{u4, u3, u2} α _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M')) f l)) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R M' M' (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')) (Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) α' (Finsupp.addCommMonoid.{u3, u2} _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')))) _inst_9 (Finsupp.module.{u3, u2, u2} _inst_1 R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Semiring.toModule.{u2} R M')) _inst_10) (Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) (fun (_x : Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) => α') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) α' M' M' (Finsupp.addCommMonoid.{u3, u2} _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')))) _inst_9 (Finsupp.module.{u3, u2, u2} _inst_1 R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Semiring.toModule.{u2} R M')) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Finsupp.total.{u3, u1, u2} _inst_1 α' R M' _inst_9 _inst_10 v') (Finsupp.equivMapDomain.{u4, u3, u2} α _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M')) f l)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u1), max (succ u4) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u4, u1} R R M' M' (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) α' (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')))) _inst_9 (Finsupp.module.{u4, u2, u2} α R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Semiring.toModule.{u2} R M')) _inst_10) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) (fun (_x : Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) => α') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u1} R R (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) α' M' M' (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')))) _inst_9 (Finsupp.module.{u4, u2, u2} α R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Semiring.toModule.{u2} R M')) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Finsupp.total.{u4, u1, u2} α α' R M' _inst_9 _inst_10 (Function.comp.{succ u4, succ u3, succ u1} α _inst_1 α' v' (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Equiv.{succ u4, succ u3} α _inst_1) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => _inst_1) _x) (Equiv.instFunLikeEquiv.{succ u4, succ u3} α _inst_1) f))) l)
Case conversion may be inaccurate. Consider using '#align finsupp.total_equiv_map_domain Finsupp.total_equivMapDomainₓ'. -/
@[simp]
theorem total_equivMapDomain (f : α ≃ α') (l : α →₀ R) :
@@ -1365,7 +1365,7 @@ theorem domLCongr_symm {α₁ α₂ : Type _} (f : α₁ ≃ α₂) :
lean 3 declaration is
forall {M : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {α₁ : Type.{u3}} {α₂ : Type.{u4}} (e : Equiv.{succ u3, succ u4} α₁ α₂) (i : α₁) (m : M), Eq.{max (succ u4) (succ u1)} (Finsupp.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (coeFn.{max (succ (max u3 u1)) (succ (max u4 u1)), max (succ (max u3 u1)) (succ (max u4 u1))} (LinearEquiv.{u2, u2, max u3 u1, max u4 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (Finsupp.{u3, u1} α₁ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.addCommMonoid.{u3, u1} α₁ M _inst_3) (Finsupp.addCommMonoid.{u4, u1} α₂ M _inst_3) (Finsupp.module.{u3, u1, u2} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u1, u2} α₂ M R _inst_1 _inst_3 _inst_4)) (fun (_x : LinearEquiv.{u2, u2, max u3 u1, max u4 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (Finsupp.{u3, u1} α₁ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.addCommMonoid.{u3, u1} α₁ M _inst_3) (Finsupp.addCommMonoid.{u4, u1} α₂ M _inst_3) (Finsupp.module.{u3, u1, u2} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u1, u2} α₂ M R _inst_1 _inst_3 _inst_4)) => (Finsupp.{u3, u1} α₁ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) -> (Finsupp.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (LinearEquiv.hasCoeToFun.{u2, u2, max u3 u1, max u4 u1} R R (Finsupp.{u3, u1} α₁ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α₁ M _inst_3) (Finsupp.addCommMonoid.{u4, u1} α₂ M _inst_3) (Finsupp.module.{u3, u1, u2} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u1, u2} α₂ M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1)) (Finsupp.domLCongr.{u1, u2, u3, u4} M R _inst_1 _inst_3 _inst_4 α₁ α₂ e) (Finsupp.single.{u3, u1} α₁ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) i m)) (Finsupp.single.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (coeFn.{max 1 (max (succ u3) (succ u4)) (succ u4) (succ u3), max (succ u3) (succ u4)} (Equiv.{succ u3, succ u4} α₁ α₂) (fun (_x : Equiv.{succ u3, succ u4} α₁ α₂) => α₁ -> α₂) (Equiv.hasCoeToFun.{succ u3, succ u4} α₁ α₂) e i) m)
but is expected to have type
- forall {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {α₁ : Type.{u4}} {α₂ : Type.{u3}} (e : Equiv.{succ u4, succ u3} α₁ α₂) (i : α₁) (m : M), Eq.{max (succ u2) (succ u3)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.single.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) i m)) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u2), max (succ u3) (succ u2)} (LinearEquiv.{u1, u1, max u2 u4, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (_x : Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _x) (SMulHomClass.toFunLike.{max (max u4 u3) u2, u1, max u4 u2, max u3 u2} (LinearEquiv.{u1, u1, max u2 u4, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R 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α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u4 u2, max u3 u2} R R (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1)))))) (Finsupp.domLCongr.{u2, u1, u4, u3} M R _inst_1 _inst_3 _inst_4 α₁ α₂ e) (Finsupp.single.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) i m)) (Finsupp.single.{u3, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α₁) => α₂) i) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Equiv.{succ u4, succ u3} α₁ α₂) α₁ (fun (_x : α₁) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α₁) => α₂) _x) (Equiv.instFunLikeEquiv.{succ u4, succ u3} α₁ α₂) e i) m)
+ forall {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {α₁ : Type.{u4}} {α₂ : Type.{u3}} (e : Equiv.{succ u4, succ u3} α₁ α₂) (i : α₁) (m : M), Eq.{max (succ u2) (succ u3)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.single.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) i m)) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u2), max (succ u3) (succ u2)} (LinearEquiv.{u1, u1, max u2 u4, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (_x : Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _x) (SMulHomClass.toFunLike.{max (max u4 u3) u2, u1, max u4 u2, max u3 u2} (LinearEquiv.{u1, u1, max u2 u4, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4)) R (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulZeroClass.toSMul.{u1, max u4 u2} R (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (AddMonoid.toZero.{max u4 u2} (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (AddCommMonoid.toAddMonoid.{max u4 u2} (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3))) (DistribSMul.toSMulZeroClass.{u1, max u4 u2} R (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (AddMonoid.toAddZeroClass.{max u4 u2} (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (AddCommMonoid.toAddMonoid.{max u4 u2} (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3))) (DistribMulAction.toDistribSMul.{u1, max u4 u2} R (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u4 u2} (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3)) (Module.toDistribMulAction.{u1, max u4 u2} R (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, max u3 u2} R (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3))) (DistribSMul.toSMulZeroClass.{u1, max u3 u2} R (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3))) (DistribMulAction.toDistribSMul.{u1, max u3 u2} R (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3)) (Module.toDistribMulAction.{u1, max u3 u2} R (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u4 u3) u2, u1, max u4 u2, max u3 u2} (LinearEquiv.{u1, u1, max u2 u4, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4)) R (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u4 u2} (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3)) (Module.toDistribMulAction.{u1, max u4 u2} R (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, max u3 u2} R (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4)) (SemilinearMapClass.distribMulActionHomClass.{u1, max u4 u2, max u3 u2, max (max u4 u3) u2} R (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (LinearEquiv.{u1, u1, max u2 u4, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4)) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u4 u2, max u3 u2, max (max u4 u3) u2} R R (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (LinearEquiv.{u1, u1, max u2 u4, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4)) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u4 u2, max u3 u2} R R (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1)))))) (Finsupp.domLCongr.{u2, u1, u4, u3} M R _inst_1 _inst_3 _inst_4 α₁ α₂ e) (Finsupp.single.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) i m)) (Finsupp.single.{u3, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α₁) => α₂) i) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Equiv.{succ u4, succ u3} α₁ α₂) α₁ (fun (_x : α₁) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α₁) => α₂) _x) (Equiv.instFunLikeEquiv.{succ u4, succ u3} α₁ α₂) e i) m)
Case conversion may be inaccurate. Consider using '#align finsupp.dom_lcongr_single Finsupp.domLCongr_singleₓ'. -/
@[simp]
theorem domLCongr_single {α₁ : Type _} {α₂ : Type _} (e : α₁ ≃ α₂) (i : α₁) (m : M) :
@@ -1533,7 +1533,7 @@ def lcongr {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N) : (ι →
lean 3 declaration is
forall {M : Type.{u1}} {N : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : Module.{u3, u2} R N _inst_1 _inst_5] {ι : Type.{u4}} {κ : Type.{u5}} (e₁ : Equiv.{succ u4, succ u5} ι κ) (e₂ : LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (i : ι) (m : M), Eq.{max (succ u5) (succ u2)} (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) (coeFn.{max (succ (max u4 u1)) (succ (max u5 u2)), max (succ (max u4 u1)) (succ (max u5 u2))} (LinearEquiv.{u3, u3, max u4 u1, max u5 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) (Finsupp.addCommMonoid.{u4, u1} ι M _inst_3) (Finsupp.addCommMonoid.{u5, u2} κ N _inst_5) (Finsupp.module.{u4, u1, u3} ι M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u5, u2, u3} κ N R _inst_1 _inst_5 _inst_6)) (fun (_x : LinearEquiv.{u3, u3, max u4 u1, max u5 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) (Finsupp.addCommMonoid.{u4, u1} ι M _inst_3) (Finsupp.addCommMonoid.{u5, u2} κ N _inst_5) (Finsupp.module.{u4, u1, u3} ι M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u5, u2, u3} κ N R _inst_1 _inst_5 _inst_6)) => (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) -> (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))))) (LinearEquiv.hasCoeToFun.{u3, u3, max u4 u1, max u5 u2} R R (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u1} ι M _inst_3) (Finsupp.addCommMonoid.{u5, u2} κ N _inst_5) (Finsupp.module.{u4, u1, u3} ι M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u5, u2, u3} κ N R _inst_1 _inst_5 _inst_6) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)) (Finsupp.lcongr.{u1, u2, u3, u4, u5} M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 ι κ e₁ e₂) (Finsupp.single.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) i m)) (Finsupp.single.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))) (coeFn.{max 1 (max (succ u4) (succ u5)) (succ u5) (succ u4), max (succ u4) (succ u5)} (Equiv.{succ u4, succ u5} ι κ) (fun (_x : Equiv.{succ u4, succ u5} ι κ) => ι -> κ) (Equiv.hasCoeToFun.{succ u4, succ u5} ι κ) e₁ i) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (_x : LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) => M -> N) (LinearEquiv.hasCoeToFun.{u3, u3, u1, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)) e₂ m))
but is expected to have type
- forall {M : Type.{u2}} {N : Type.{u1}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : Module.{u3, u1} R N _inst_1 _inst_5] {ι : Type.{u5}} {κ : Type.{u4}} (e₁ : Equiv.{succ u5, succ u4} ι κ) (e₂ : LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (i : ι) (m : M), Eq.{max (succ u1) (succ u4)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (Finsupp.single.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) i m)) 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+ forall {M : Type.{u2}} {N : Type.{u1}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : Module.{u3, u1} R N _inst_1 _inst_5] {ι : Type.{u5}} {κ : Type.{u4}} (e₁ : Equiv.{succ u5, succ u4} ι κ) (e₂ : LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (i : ι) (m : M), Eq.{max (succ u1) (succ u4)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (Finsupp.single.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) i m)) 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(AddCommMonoid.toAddMonoid.{u1} N _inst_5))) _inst_1 (Finsupp.addCommMonoid.{u4, u1} κ N _inst_5) (Finsupp.module.{u4, u1, u3} κ N R _inst_1 _inst_5 _inst_6)) (SemilinearMapClass.distribMulActionHomClass.{u3, max u2 u5, max u1 u4, max (max (max u2 u1) u4) u5} R (Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (LinearEquiv.{u3, u3, max u2 u5, max u1 u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (Finsupp.addCommMonoid.{u5, u2} ι M _inst_3) (Finsupp.addCommMonoid.{u4, u1} κ N _inst_5) 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(SMulZeroClass.toSMul.{u3, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (DistribSMul.toSMulZeroClass.{u3, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (DistribMulAction.toDistribSMul.{u3, u2} R M (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} M _inst_3) (Module.toDistribMulAction.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u3, u1} R N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5)) (DistribSMul.toSMulZeroClass.{u3, u1} R N (AddMonoid.toAddZeroClass.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5)) (DistribMulAction.toDistribSMul.{u3, u1} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_5) (Module.toDistribMulAction.{u3, u1} R N _inst_1 _inst_5 _inst_6)))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (LinearEquiv.{u3, u3, u2, 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Case conversion may be inaccurate. Consider using '#align finsupp.lcongr_single Finsupp.lcongr_singleₓ'. -/
@[simp]
theorem lcongr_single {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N) (i : ι) (m : M) :
@@ -1544,7 +1544,7 @@ theorem lcongr_single {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N)
lean 3 declaration is
forall {M : Type.{u1}} {N : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : Module.{u3, u2} R N _inst_1 _inst_5] {ι : Type.{u4}} {κ : Type.{u5}} (e₁ : Equiv.{succ u4, succ u5} ι κ) (e₂ : LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (f : Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (k : κ), Eq.{succ u2} N (coeFn.{max (succ u5) (succ u2), max (succ u5) (succ u2)} (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) (fun (_x : Finsupp.{u5, u2} κ N 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but is expected to have type
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(Equiv.symm.{succ u5, succ u4} ι κ e₁) k)))
+ forall {M : Type.{u2}} {N : Type.{u1}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : Module.{u3, u1} R N _inst_1 _inst_5] {ι : Type.{u5}} {κ : Type.{u4}} (e₁ : Equiv.{succ u5, succ u4} ι κ) (e₂ : LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (f : Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (k : κ), Eq.{succ u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : κ) => N) k) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) κ (fun (_x : κ) => (fun 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_inst_5))) (AddMonoid.toZero.{max u1 u4} (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (Finsupp.addCommMonoid.{u4, u1} κ N _inst_5))) (DistribSMul.toSMulZeroClass.{u3, max u1 u4} R (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (AddMonoid.toAddZeroClass.{max u1 u4} (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (Finsupp.addCommMonoid.{u4, u1} κ N _inst_5))) (DistribMulAction.toDistribSMul.{u3, max u1 u4} R (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (Finsupp.addCommMonoid.{u4, u1} κ N _inst_5)) (Module.toDistribMulAction.{u3, max u1 u4} R (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) _inst_1 (Finsupp.addCommMonoid.{u4, u1} κ N _inst_5) (Finsupp.module.{u4, u1, u3} κ N R _inst_1 _inst_5 _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max (max (max u2 u1) u5) u4, u3, max u2 u5, max u1 u4} (LinearEquiv.{u3, u3, max u2 u5, max u1 u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) 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(AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u5, u2} ι M _inst_3) (Finsupp.addCommMonoid.{u4, u1} κ N _inst_5) (Finsupp.module.{u5, u2, u3} ι M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u1, u3} κ N R _inst_1 _inst_5 _inst_6) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)))))) (Finsupp.lcongr.{u2, u1, u3, u5, u4} M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 ι κ e₁ e₂) f) k) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M) => N) _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) R M N (SMulZeroClass.toSMul.{u3, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (DistribSMul.toSMulZeroClass.{u3, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (DistribMulAction.toDistribSMul.{u3, u2} R M (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} M _inst_3) (Module.toDistribMulAction.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u3, u1} R N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5)) (DistribSMul.toSMulZeroClass.{u3, u1} R N (AddMonoid.toAddZeroClass.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5)) (DistribMulAction.toDistribSMul.{u3, u1} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_5) (Module.toDistribMulAction.{u3, u1} R N _inst_1 _inst_5 _inst_6)))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) R M N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} M _inst_3) (AddCommMonoid.toAddMonoid.{u1} N _inst_5) (Module.toDistribMulAction.{u3, u2} R M _inst_1 _inst_3 _inst_4) (Module.toDistribMulAction.{u3, u1} R N _inst_1 _inst_5 _inst_6) (SemilinearMapClass.distribMulActionHomClass.{u3, u2, u1, max u2 u1} R M N (LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (SemilinearEquivClass.instSemilinearMapClass.{u3, u3, u2, u1, max u2 u1} R R M N (LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, u2, u1} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)))))) e₂ (FunLike.coe.{max (succ u5) (succ u2), succ u5, succ u2} (Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => M) _x) (Finsupp.funLike.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) f (FunLike.coe.{max (succ u5) (succ u4), succ u4, succ u5} (Equiv.{succ u4, succ u5} κ ι) κ (fun (_x : κ) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : κ) => ι) _x) (Equiv.instFunLikeEquiv.{succ u4, succ u5} κ ι) (Equiv.symm.{succ u5, succ u4} ι κ e₁) k)))
Case conversion may be inaccurate. Consider using '#align finsupp.lcongr_apply_apply Finsupp.lcongr_apply_applyₓ'. -/
@[simp]
theorem lcongr_apply_apply {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N) (f : ι →₀ M) (k : κ) :
@@ -1556,7 +1556,7 @@ theorem lcongr_apply_apply {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[
lean 3 declaration is
forall {M : Type.{u1}} {N : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : Module.{u3, u2} R N _inst_1 _inst_5] {ι : Type.{u4}} {κ : Type.{u5}} (e₁ : Equiv.{succ u4, succ u5} ι κ) (e₂ : LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (k : κ) (n : N), Eq.{max (succ u4) (succ u1)} (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (coeFn.{max (succ (max u5 u2)) (succ (max u4 u1)), max (succ (max u5 u2)) (succ (max u4 u1))} (LinearEquiv.{u3, u3, max u5 u2, max u4 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R 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(AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.addCommMonoid.{u5, u2} κ N _inst_5) (Finsupp.addCommMonoid.{u4, u1} ι M _inst_3) (Finsupp.module.{u5, u2, u3} κ N R _inst_1 _inst_5 _inst_6) (Finsupp.module.{u4, u1, u3} ι M R _inst_1 _inst_3 _inst_4)) => (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) -> (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (LinearEquiv.hasCoeToFun.{u3, u3, max u5 u2, max u4 u1} R R (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u5, u2} κ N _inst_5) (Finsupp.addCommMonoid.{u4, u1} ι M _inst_3) (Finsupp.module.{u5, u2, u3} κ N R _inst_1 _inst_5 _inst_6) (Finsupp.module.{u4, u1, u3} ι M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)) (LinearEquiv.symm.{u3, u3, max u4 u1, max u5 u2} R R (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u1} ι M _inst_3) (Finsupp.addCommMonoid.{u5, u2} κ N _inst_5) (Finsupp.module.{u4, u1, u3} ι M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u5, u2, u3} κ N R _inst_1 _inst_5 _inst_6) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.lcongr.{u1, u2, u3, u4, u5} M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 ι κ e₁ e₂)) (Finsupp.single.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))) k n)) (Finsupp.single.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (coeFn.{max 1 (max (succ u5) (succ u4)) (succ u4) (succ u5), max (succ u5) (succ u4)} (Equiv.{succ u5, succ u4} κ ι) (fun (_x : Equiv.{succ u5, succ u4} κ ι) => κ -> ι) (Equiv.hasCoeToFun.{succ u5, succ u4} κ ι) (Equiv.symm.{succ u4, succ u5} ι κ e₁) k) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) N M _inst_5 _inst_3 _inst_6 _inst_4) (fun (_x : LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) N M _inst_5 _inst_3 _inst_6 _inst_4) => N -> M) (LinearEquiv.hasCoeToFun.{u3, u3, u2, u1} R R N M _inst_1 _inst_1 _inst_5 _inst_3 _inst_6 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)) (LinearEquiv.symm.{u3, u3, u1, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) e₂) n))
but is expected to have type
- forall {M : Type.{u2}} {N : Type.{u1}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : Module.{u3, u1} R N _inst_1 _inst_5] {ι : Type.{u5}} {κ : Type.{u4}} (e₁ : Equiv.{succ u5, succ u4} ι κ) (e₂ : LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (k : κ) (n : N), Eq.{max (succ u2) (succ u5)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) => Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.single.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5)) k n)) 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_inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u1} κ N _inst_5) (Finsupp.addCommMonoid.{u5, u2} ι M _inst_3) (Finsupp.module.{u4, u1, u3} κ N R _inst_1 _inst_5 _inst_6) (Finsupp.module.{u5, u2, u3} ι M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)))))) (LinearEquiv.symm.{u3, u3, max u2 u5, max u1 u4} R R (Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u5, u2} ι M _inst_3) (Finsupp.addCommMonoid.{u4, u1} κ N _inst_5) (Finsupp.module.{u5, u2, u3} ι M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u1, u3} κ N R _inst_1 _inst_5 _inst_6) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.lcongr.{u2, u1, u3, u5, u4} M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 ι κ e₁ e₂)) (Finsupp.single.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5)) k n)) (Finsupp.single.{u5, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : κ) => ι) k) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : N) => M) n) (AddMonoid.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : N) => M) n) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : N) => M) n) _inst_3)) (FunLike.coe.{max (succ u4) (succ u5), succ u4, succ u5} (Equiv.{succ u4, succ u5} κ ι) κ (fun (_x : κ) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : κ) => ι) _x) (Equiv.instFunLikeEquiv.{succ u4, succ u5} κ ι) (Equiv.symm.{succ u5, succ u4} ι κ e₁) k) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) N M _inst_5 _inst_3 _inst_6 _inst_4) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : N) => M) _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u1, u2} (LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) N M _inst_5 _inst_3 _inst_6 _inst_4) R N M (SMulZeroClass.toSMul.{u3, u1} R N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5)) (DistribSMul.toSMulZeroClass.{u3, u1} R N (AddMonoid.toAddZeroClass.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5)) (DistribMulAction.toDistribSMul.{u3, u1} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_5) (Module.toDistribMulAction.{u3, u1} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u3, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (DistribSMul.toSMulZeroClass.{u3, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (DistribMulAction.toDistribSMul.{u3, u2} R M (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} M _inst_3) (Module.toDistribMulAction.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u1, u2} (LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) N M _inst_5 _inst_3 _inst_6 _inst_4) R N M (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_5) (AddCommMonoid.toAddMonoid.{u2} M _inst_3) (Module.toDistribMulAction.{u3, u1} R N _inst_1 _inst_5 _inst_6) (Module.toDistribMulAction.{u3, u2} R M _inst_1 _inst_3 _inst_4) (SemilinearMapClass.distribMulActionHomClass.{u3, u1, u2, max u2 u1} R N M (LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) N M _inst_5 _inst_3 _inst_6 _inst_4) _inst_1 _inst_5 _inst_3 _inst_6 _inst_4 (SemilinearEquivClass.instSemilinearMapClass.{u3, u3, u1, u2, max u2 u1} R R N M (LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) N M _inst_5 _inst_3 _inst_6 _inst_4) _inst_1 _inst_1 _inst_5 _inst_3 _inst_6 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, u1, u2} R R N M _inst_1 _inst_1 _inst_5 _inst_3 _inst_6 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)))))) (LinearEquiv.symm.{u3, u3, u2, u1} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) e₂) n))
+ forall {M : Type.{u2}} {N : Type.{u1}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : Module.{u3, u1} R N _inst_1 _inst_5] {ι : Type.{u5}} {κ : Type.{u4}} (e₁ : Equiv.{succ u5, succ u4} ι κ) (e₂ : LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (k : κ) (n : N), Eq.{max (succ u2) (succ u5)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) => Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.single.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5)) k n)) 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(MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_5) (Module.toDistribMulAction.{u3, u1} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u3, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (DistribSMul.toSMulZeroClass.{u3, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (DistribMulAction.toDistribSMul.{u3, u2} R M (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} M _inst_3) (Module.toDistribMulAction.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u1, u2} (LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) N M _inst_5 _inst_3 _inst_6 _inst_4) R N M (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_5) (AddCommMonoid.toAddMonoid.{u2} M _inst_3) (Module.toDistribMulAction.{u3, u1} R N _inst_1 _inst_5 _inst_6) (Module.toDistribMulAction.{u3, u2} R M _inst_1 _inst_3 _inst_4) (SemilinearMapClass.distribMulActionHomClass.{u3, u1, u2, max u2 u1} R N M (LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) N M _inst_5 _inst_3 _inst_6 _inst_4) _inst_1 _inst_5 _inst_3 _inst_6 _inst_4 (SemilinearEquivClass.instSemilinearMapClass.{u3, u3, u1, u2, max u2 u1} R R N M (LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) N M _inst_5 _inst_3 _inst_6 _inst_4) _inst_1 _inst_1 _inst_5 _inst_3 _inst_6 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, u1, u2} R R N M _inst_1 _inst_1 _inst_5 _inst_3 _inst_6 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)))))) (LinearEquiv.symm.{u3, u3, u2, u1} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) e₂) n))
Case conversion may be inaccurate. Consider using '#align finsupp.lcongr_symm_single Finsupp.lcongr_symm_singleₓ'. -/
theorem lcongr_symm_single {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N) (k : κ) (n : N) :
(lcongr e₁ e₂).symm (Finsupp.single k n) = Finsupp.single (e₁.symm k) (e₂.symm n) :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/c89fe2d59ae06402c3f55f978016d1ada444f57e
@@ -91,7 +91,7 @@ def lsingle (a : α) : M →ₗ[R] α →₀ M :=
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} [_inst_1 : Semiring.{u4} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] {{φ : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6}} {{ψ : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6}}, (forall (a : α) (b : M), Eq.{succ u3} N (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (fun (_x : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) => (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) -> N) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) φ (Finsupp.single.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) a b)) (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (fun (_x : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) => (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) -> N) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) ψ (Finsupp.single.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) a b))) -> (Eq.{max (succ (max u1 u2)) (succ u3)} (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) φ ψ)
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u3}} {N : Type.{u1}} {R : Type.{u4}} [_inst_1 : Semiring.{u4} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u4, u3} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : Module.{u4, u1} R N _inst_1 _inst_5] {{φ : LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6}} {{ψ : LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6}}, (forall (a : α) (b : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => N) (Finsupp.single.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) a b)) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u3), succ u1} (LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (fun (_x : Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u2 u3, u1} R R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) φ (Finsupp.single.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) a b)) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u3), succ u1} (LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (fun (_x : Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u2 u3, u1} R R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) ψ (Finsupp.single.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) a b))) -> (Eq.{max (max (succ u2) (succ u3)) (succ u1)} (LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) φ ψ)
+ forall {α : Type.{u2}} {M : Type.{u3}} {N : Type.{u1}} {R : Type.{u4}} [_inst_1 : Semiring.{u4} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u4, u3} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : Module.{u4, u1} R N _inst_1 _inst_5] {{φ : LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6}} {{ψ : LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6}}, (forall (a : α) (b : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => N) (Finsupp.single.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) a b)) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u3), succ u1} (LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (fun (_x : Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u2 u3, u1} R R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) φ (Finsupp.single.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) a b)) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u3), succ u1} (LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (fun (_x : Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u2 u3, u1} R R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) ψ (Finsupp.single.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) a b))) -> (Eq.{max (max (succ u2) (succ u3)) (succ u1)} (LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) φ ψ)
Case conversion may be inaccurate. Consider using '#align finsupp.lhom_ext Finsupp.lhom_extₓ'. -/
/-- Two `R`-linear maps from `finsupp X M` which agree on each `single x y` agree everywhere. -/
theorem lhom_ext ⦃φ ψ : (α →₀ M) →ₗ[R] N⦄ (h : ∀ a b, φ (single a b) = ψ (single a b)) : φ = ψ :=
@@ -168,7 +168,7 @@ def lsubtypeDomain : (α →₀ M) →ₗ[R] s →₀ M
lean 3 declaration is
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but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (f : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Finsupp.{u3, u2} (Set.Elem.{u3} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) f) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearMap.{u1, u1, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} (Set.Elem.{u3} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} (Set.Elem.{u3} α s) M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} (Set.Elem.{u3} α s) M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (_x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Finsupp.{u3, u2} (Set.Elem.{u3} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u2, max u3 u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} (Set.Elem.{u3} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} (Set.Elem.{u3} α s) M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} (Set.Elem.{u3} α s) M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lsubtypeDomain.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) f) (Finsupp.subtypeDomain.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (fun (x : α) => Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) x s) f)
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (f : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Finsupp.{u3, u2} (Set.Elem.{u3} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) f) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearMap.{u1, u1, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} (Set.Elem.{u3} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} (Set.Elem.{u3} α s) M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} (Set.Elem.{u3} α s) M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (_x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Finsupp.{u3, u2} (Set.Elem.{u3} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u2, max u3 u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} (Set.Elem.{u3} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} (Set.Elem.{u3} α s) M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} (Set.Elem.{u3} α s) M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lsubtypeDomain.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) f) (Finsupp.subtypeDomain.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (fun (x : α) => Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) x s) f)
Case conversion may be inaccurate. Consider using '#align finsupp.lsubtype_domain_apply Finsupp.lsubtypeDomain_applyₓ'. -/
theorem lsubtypeDomain_apply (f : α →₀ M) :
(lsubtypeDomain s : (α →₀ M) →ₗ[R] s →₀ M) f = subtypeDomain (fun x => x ∈ s) f :=
@@ -181,7 +181,7 @@ end LsubtypeDomain
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (a : α) (b : M), Eq.{max (succ u1) (succ u2)} (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (fun (_x : LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) => M -> (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))))) (LinearMap.hasCoeToFun.{u3, u3, u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lsingle.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a) b) (Finsupp.single.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) a b)
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (a : α) (b : M), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) b) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a) b) (Finsupp.single.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) a b)
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (a : α) (b : M), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) b) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a) b) (Finsupp.single.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) a b)
Case conversion may be inaccurate. Consider using '#align finsupp.lsingle_apply Finsupp.lsingle_applyₓ'. -/
@[simp]
theorem lsingle_apply (a : α) (b : M) : (lsingle a : M →ₗ[R] α →₀ M) b = single a b :=
@@ -192,7 +192,7 @@ theorem lsingle_apply (a : α) (b : M) : (lsingle a : M →ₗ[R] α →₀ M) b
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (a : α) (f : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))), Eq.{succ u2} M (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (LinearMap.{u3, u3, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4) => (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u2, u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lapply.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a) f) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (fun (_x : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) => α -> M) (Finsupp.coeFun.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) f a)
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (a : α) (f : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => M) f) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), succ u2} (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (_x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u2, u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lapply.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a) f) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) α (fun (_x : α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) _x) (Finsupp.funLike.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) f a)
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (a : α) (f : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => M) f) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), succ u2} (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (_x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u2, u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lapply.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a) f) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) α (fun (_x : α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) _x) (Finsupp.funLike.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) f a)
Case conversion may be inaccurate. Consider using '#align finsupp.lapply_apply Finsupp.lapply_applyₓ'. -/
@[simp]
theorem lapply_apply (a : α) (f : α →₀ M) : (lapply a : (α →₀ M) →ₗ[R] M) f = f a :=
@@ -203,7 +203,7 @@ theorem lapply_apply (a : α) (f : α →₀ M) : (lapply a : (α →₀ M) →
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (a : α), Eq.{succ u2} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) (LinearMap.ker.{u3, u3, u2, max u1 u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u3, u3, u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lsingle.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a)) (Bot.bot.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasBot.{u3, u2} R M _inst_1 _inst_3 _inst_4))
but is expected to have type
- forall {α : Type.{u1}} {M : Type.{u3}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_1 _inst_3] (a : α), Eq.{succ u3} (Submodule.{u2, u3} R M _inst_1 _inst_3 _inst_4) (LinearMap.ker.{u2, u2, u3, max u1 u3, max u1 u3} R R M (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u3} α M _inst_3) _inst_4 (Finsupp.module.{u1, u3, u2} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u1, u3} α M _inst_3) _inst_4 (Finsupp.module.{u1, u3, u2} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u3, max u1 u3} R R M (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u3} α M _inst_3) _inst_4 (Finsupp.module.{u1, u3, u2} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.lsingle.{u1, u3, u2} α M R _inst_1 _inst_3 _inst_4 a)) (Bot.bot.{u3} (Submodule.{u2, u3} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u2, u3} R M _inst_1 _inst_3 _inst_4))
+ forall {α : Type.{u1}} {M : Type.{u3}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_1 _inst_3] (a : α), Eq.{succ u3} (Submodule.{u2, u3} R M _inst_1 _inst_3 _inst_4) (LinearMap.ker.{u2, u2, u3, max u1 u3, max u1 u3} R R M (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u3} α M _inst_3) _inst_4 (Finsupp.module.{u1, u3, u2} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u1, u3} α M _inst_3) _inst_4 (Finsupp.module.{u1, u3, u2} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u2, u2, u3, max u1 u3} R R M (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u3} α M _inst_3) _inst_4 (Finsupp.module.{u1, u3, u2} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.lsingle.{u1, u3, u2} α M R _inst_1 _inst_3 _inst_4 a)) (Bot.bot.{u3} (Submodule.{u2, u3} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u2, u3} R M _inst_1 _inst_3 _inst_4))
Case conversion may be inaccurate. Consider using '#align finsupp.ker_lsingle Finsupp.ker_lsingleₓ'. -/
@[simp]
theorem ker_lsingle (a : α) : (lsingle a : M →ₗ[R] α →₀ M).ker = ⊥ :=
@@ -214,7 +214,7 @@ theorem ker_lsingle (a : α) : (lsingle a : M →ₗ[R] α →₀ M).ker = ⊥ :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α) (t : Set.{u1} α), (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) s t) -> (LE.le.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toHasLe.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))))) (iSup.{max u1 u2, succ u1} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => iSup.{max u1 u2, 0} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LinearMap.range.{u3, u3, u2, max u1 u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u3, u3, u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R _inst_1) (Finsupp.lsingle.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a)))) (iInf.{max u1 u2, succ u1} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasInf.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) α (fun (a : α) => iInf.{max u1 u2, 0} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasInf.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a t) => LinearMap.ker.{u3, u3, max u1 u2, u2, max u1 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4) (LinearMap.semilinearMapClass.{u3, u3, max u1 u2, u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lapply.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a)))))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (t : Set.{u3} α), (Disjoint.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} α) (Preorder.toLE.{u3} (Set.{u3} α) (PartialOrder.toPreorder.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) s t) -> (LE.le.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toLE.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))))) (iSup.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => iSup.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) (fun (H : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a)))) (iInf.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) α (fun (a : α) => iInf.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a t) (fun (H : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a t) => LinearMap.ker.{u1, u1, max u3 u2, u2, max u3 u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u3 u2, u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lapply.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a)))))
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (t : Set.{u3} α), (Disjoint.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} α) (Preorder.toLE.{u3} (Set.{u3} α) (PartialOrder.toPreorder.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) s t) -> (LE.le.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toLE.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))))) (iSup.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => iSup.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) (fun (H : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a)))) (iInf.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) α (fun (a : α) => iInf.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a t) (fun (H : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a t) => LinearMap.ker.{u1, u1, max u3 u2, u2, max u3 u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4) (LinearMap.semilinearMapClass.{u1, u1, max u3 u2, u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lapply.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a)))))
Case conversion may be inaccurate. Consider using '#align finsupp.lsingle_range_le_ker_lapply Finsupp.lsingle_range_le_ker_lapplyₓ'. -/
theorem lsingle_range_le_ker_lapply (s t : Set α) (h : Disjoint s t) :
(⨆ a ∈ s, (lsingle a : M →ₗ[R] α →₀ M).range) ≤ ⨅ a ∈ t, ker (lapply a : (α →₀ M) →ₗ[R] M) :=
@@ -230,7 +230,7 @@ theorem lsingle_range_le_ker_lapply (s t : Set α) (h : Disjoint s t) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], LE.le.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toHasLe.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))))) (iInf.{max u1 u2, succ u1} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasInf.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) α (fun (a : α) => LinearMap.ker.{u3, u3, max u1 u2, u2, max u1 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4) (LinearMap.semilinearMapClass.{u3, u3, max u1 u2, u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lapply.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a))) (Bot.bot.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasBot.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], LE.le.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toLE.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))))) (iInf.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) α (fun (a : α) => LinearMap.ker.{u1, u1, max u3 u2, u2, max u3 u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u3 u2, u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lapply.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a))) (Bot.bot.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instBotSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], LE.le.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toLE.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))))) (iInf.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) α (fun (a : α) => LinearMap.ker.{u1, u1, max u3 u2, u2, max u3 u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4) (LinearMap.semilinearMapClass.{u1, u1, max u3 u2, u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lapply.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a))) (Bot.bot.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instBotSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))
Case conversion may be inaccurate. Consider using '#align finsupp.infi_ker_lapply_le_bot Finsupp.iInf_ker_lapply_le_botₓ'. -/
theorem iInf_ker_lapply_le_bot : (⨅ a, ker (lapply a : (α →₀ M) →ₗ[R] M)) ≤ ⊥ :=
by
@@ -242,7 +242,7 @@ theorem iInf_ker_lapply_le_bot : (⨅ a, ker (lapply a : (α →₀ M) →ₗ[R]
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], Eq.{succ (max u1 u2)} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (iSup.{max u1 u2, succ u1} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => LinearMap.range.{u3, u3, u2, max u1 u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u3, u3, u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R _inst_1) (Finsupp.lsingle.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a))) (Top.top.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasTop.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (iSup.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a))) (Top.top.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instTopSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (iSup.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a))) (Top.top.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instTopSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))
Case conversion may be inaccurate. Consider using '#align finsupp.supr_lsingle_range Finsupp.iSup_lsingle_rangeₓ'. -/
theorem iSup_lsingle_range : (⨆ a, (lsingle a : M →ₗ[R] α →₀ M).range) = ⊤ :=
by
@@ -255,7 +255,7 @@ theorem iSup_lsingle_range : (⨆ a, (lsingle a : M →ₗ[R] α →₀ M).range
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α) (t : Set.{u1} α), (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) s t) -> (Disjoint.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) (Submodule.orderBot.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (iSup.{max u1 u2, succ u1} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => iSup.{max u1 u2, 0} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LinearMap.range.{u3, u3, u2, max u1 u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u3, u3, u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R _inst_1) (Finsupp.lsingle.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a)))) (iSup.{max u1 u2, succ u1} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => iSup.{max u1 u2, 0} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a t) => LinearMap.range.{u3, u3, u2, max u1 u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u3, u3, u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R _inst_1) (Finsupp.lsingle.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a)))))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (t : Set.{u3} α), (Disjoint.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} α) (Preorder.toLE.{u3} (Set.{u3} α) (PartialOrder.toPreorder.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) s t) -> (Disjoint.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (iSup.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => iSup.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) (fun (H : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a)))) (iSup.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => iSup.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a t) (fun (H : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a t) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a)))))
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (t : Set.{u3} α), (Disjoint.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} α) (Preorder.toLE.{u3} (Set.{u3} α) (PartialOrder.toPreorder.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) s t) -> (Disjoint.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (iSup.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => iSup.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) (fun (H : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a)))) (iSup.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => iSup.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a t) (fun (H : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a t) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a)))))
Case conversion may be inaccurate. Consider using '#align finsupp.disjoint_lsingle_lsingle Finsupp.disjoint_lsingle_lsingleₓ'. -/
theorem disjoint_lsingle_lsingle (s t : Set α) (hs : Disjoint s t) :
Disjoint (⨆ a ∈ s, (lsingle a : M →ₗ[R] α →₀ M).range)
@@ -279,7 +279,7 @@ theorem disjoint_lsingle_lsingle (s t : Set α) (hs : Disjoint s t) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u2} M) (a : α), Eq.{succ (max u1 u2)} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.span.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Set.image.{u2, max u1 u2} M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.single.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) a) s)) (Submodule.map.{u3, u3, u2, max u1 u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomSurjective.ids.{u3} R _inst_1) (LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u3, u3, u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lsingle.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a) (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 s))
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u3}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u1, u3} R M _inst_1 _inst_3] (s : Set.{u3} M) (a : α), Eq.{max (succ u2) (succ u3)} (Submodule.{u1, max u3 u2} R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) (Finsupp.module.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.span.{u1, max u3 u2} R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) (Finsupp.module.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4) (Set.image.{u3, max u3 u2} M (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.single.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) a) s)) (Submodule.map.{u1, u1, u3, max u2 u3, max u2 u3} R R M (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_4 (Finsupp.module.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.{u1, u1, u3, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_4 (Finsupp.module.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u3, max u2 u3} R R M (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_4 (Finsupp.module.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lsingle.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4 a) (Submodule.span.{u1, u3} R M _inst_1 _inst_3 _inst_4 s))
+ forall {α : Type.{u2}} {M : Type.{u3}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u1, u3} R M _inst_1 _inst_3] (s : Set.{u3} M) (a : α), Eq.{max (succ u2) (succ u3)} (Submodule.{u1, max u3 u2} R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) (Finsupp.module.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.span.{u1, max u3 u2} R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) (Finsupp.module.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4) (Set.image.{u3, max u3 u2} M (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.single.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) a) s)) (Submodule.map.{u1, u1, u3, max u2 u3, max u2 u3} R R M (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_4 (Finsupp.module.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.{u1, u1, u3, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_4 (Finsupp.module.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u1, u1, u3, max u2 u3} R R M (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_4 (Finsupp.module.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lsingle.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4 a) (Submodule.span.{u1, u3} R M _inst_1 _inst_3 _inst_4 s))
Case conversion may be inaccurate. Consider using '#align finsupp.span_single_image Finsupp.span_single_imageₓ'. -/
theorem span_single_image (s : Set M) (a : α) :
Submodule.span R (single a '' s) = (Submodule.span R s).map (lsingle a : M →ₗ[R] α →₀ M) := by
@@ -399,7 +399,7 @@ section
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α) (l : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))), Eq.{max (succ u1) (succ u2)} (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) ((fun (a : Type.{max u1 u2}) (b : Sort.{max (succ u1) (succ u2)}) [self : HasLiftT.{succ (max u1 u2), max (succ u1) (succ u2)} a b] => self.0) (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (HasLiftT.mk.{succ (max u1 u2), max (succ u1) (succ u2)} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (CoeTCₓ.coe.{succ (max u1 u2), max (succ u1) (succ u2)} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (coeBase.{succ (max u1 u2), max (succ u1) (succ u2)} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (coeSubtype.{max (succ u1) (succ u2)} (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (fun (x : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) => Membership.Mem.{max u1 u2, max u1 u2} (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 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(Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Submodule.addCommMonoid.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Submodule.module.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.restrictDom.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) l)) (Finsupp.filter.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (fun (_x : α) => Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) _x s) l)
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (l : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))), Eq.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Subtype.val.{succ (max u3 u2)} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u3 u2, max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Set.{max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Set.instMembershipSet.{max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) x (SetLike.coe.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.setLike.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s))) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearMap.{u1, u1, max u2 u3, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Subtype.{succ (max 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α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (_x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Subtype.{succ (max u3 u2)} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u3 u2, max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.setLike.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) x (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u2, max u3 u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Subtype.{succ (max u3 u2)} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u3 u2, max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.setLike.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) x (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Submodule.addCommMonoid.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Submodule.module.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.restrictDom.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) l)) (Finsupp.filter.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (fun (_x : α) => Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) _x s) l)
Case conversion may be inaccurate. Consider using '#align finsupp.restrict_dom_apply Finsupp.restrictDom_applyₓ'. -/
@[simp]
theorem restrictDom_apply (s : Set α) (l : α →₀ M) :
@@ -427,7 +427,7 @@ theorem restrictDom_comp_subtype (s : Set α) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α), Eq.{succ (max u1 u2)} (Submodule.{u3, max u1 u2} R (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) _inst_1 (Submodule.addCommMonoid.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Submodule.module.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, 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but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α), Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u3 u2} R (Subtype.{succ (max u3 u2)} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u3 u2, max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) 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(Finsupp.restrictDom.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (Top.top.{max u3 u2} (Submodule.{u1, max u3 u2} R (Subtype.{succ (max u3 u2)} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u3 u2, max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) 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+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α), Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u3 u2} R (Subtype.{succ (max u3 u2)} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u3 u2, max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) 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Case conversion may be inaccurate. Consider using '#align finsupp.range_restrict_dom Finsupp.range_restrictDomₓ'. -/
theorem range_restrictDom (s : Set α) : (restrictDom M R s).range = ⊤ :=
range_eq_top.2 <|
@@ -608,7 +608,7 @@ def lsum : (α → M →ₗ[R] N) ≃ₗ[S] (α →₀ M) →ₗ[R] N
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toHasSmul.{u4, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u4, u3} R N (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u5, u3} S N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u5, u3} S N (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)), Eq.{max (max (succ u1) (succ u2)) (succ u3)} ((fun (_x : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) => (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) -> N) (coeFn.{max (succ (max u1 u2 u3)) (succ (max (max u1 u2) u3)), max (succ (max u1 u2 u3)) (succ (max (max u1 u2) u3))} (LinearEquiv.{u5, u5, max u1 u2 u3, max (max u1 u2) u3} S S _inst_2 _inst_2 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S 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=> LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.Function.module.{u1, u5, max u2 u3} α S (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.module.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.module.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2)) (Finsupp.lsum.{u1, u2, u3, u4, u5} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f)) (fun (d : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) => Finsupp.sum.{u1, u2, u3} α M N (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_5 d (fun (i : α) => coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (_x : LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) => M -> N) (LinearMap.hasCoeToFun.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (f i)))
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u4}} {N : Type.{u3}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u3} R S N (SMulZeroClass.toSMul.{u5, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)), Eq.{max (max (succ u2) (succ u4)) (succ u3)} (forall (a : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) a) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) 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LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R 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_inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M 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_inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f)) (fun (d : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => Finsupp.sum.{u2, u4, u3} α M ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) d) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) _inst_5 d (fun (i : α) => FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f i)))
+ forall {α : Type.{u2}} {M : Type.{u4}} {N : Type.{u3}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u3} R S N (SMulZeroClass.toSMul.{u5, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)), Eq.{max (max (succ u2) (succ u4)) (succ u3)} (forall (a : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) a) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) f) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (fun (_x : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (fun (_x : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _x) (SMulHomClass.toFunLike.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} 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_inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R 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_inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f)) (fun (d : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => Finsupp.sum.{u2, u4, u3} α M ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) d) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) _inst_5 d (fun (i : α) => FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f i)))
Case conversion may be inaccurate. Consider using '#align finsupp.coe_lsum Finsupp.coe_lsumₓ'. -/
@[simp]
theorem coe_lsum (f : α → M →ₗ[R] N) : (lsum S f : (α →₀ M) → N) = fun d => d.Sum fun i => f i :=
@@ -619,7 +619,7 @@ theorem coe_lsum (f : α → M →ₗ[R] N) : (lsum S f : (α →₀ M) → N) =
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toHasSmul.{u4, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u4, u3} R N (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u5, u3} S N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u5, u3} S N (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (l : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))), Eq.{succ u3} N (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (fun (_x : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) => (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) -> N) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (coeFn.{max (succ (max u1 u2 u3)) (succ (max (max u1 u2) u3)), max (succ (max u1 u2 u3)) (succ (max (max u1 u2) u3))} (LinearEquiv.{u5, u5, max u1 u2 u3, max (max u1 u2) u3} S S _inst_2 _inst_2 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2) (α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 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but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u4}} {N : Type.{u3}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u3} R S N (SMulZeroClass.toSMul.{u5, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (l : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) l) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), succ u3} ((fun 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_inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 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(AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2} S S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f) l) (Finsupp.sum.{u2, u4, u3} α M N (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) _inst_5 l (fun (b : α) => FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f b)))
+ forall {α : Type.{u2}} {M : Type.{u4}} {N : Type.{u3}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u3} R S N (SMulZeroClass.toSMul.{u5, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (l : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) l) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) f) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (fun (_x : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (fun (_x : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _x) (SMulHomClass.toFunLike.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M 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_inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f) l) (Finsupp.sum.{u2, u4, u3} α M N (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) _inst_5 l (fun (b : α) => FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f b)))
Case conversion may be inaccurate. Consider using '#align finsupp.lsum_apply Finsupp.lsum_applyₓ'. -/
theorem lsum_apply (f : α → M →ₗ[R] N) (l : α →₀ M) : Finsupp.lsum S f l = l.Sum fun b => f b :=
rfl
@@ -629,7 +629,7 @@ theorem lsum_apply (f : α → M →ₗ[R] N) (l : α →₀ M) : Finsupp.lsum S
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toHasSmul.{u4, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u4, u3} R N (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u5, u3} S N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u5, u3} S N (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (i : α) (m : M), Eq.{succ u3} N (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (fun (_x : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) => (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M 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but is expected to have type
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(Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) 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(Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M 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u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2} S S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f) (Finsupp.single.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) i m)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f i) m)
+ forall {α : Type.{u2}} {M : Type.{u4}} {N : Type.{u3}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u3} R S N (SMulZeroClass.toSMul.{u5, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (i : α) (m : M), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) (Finsupp.single.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) i m)) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), succ u3} 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(Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) 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u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 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_inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f) (Finsupp.single.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) i m)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f i) m)
Case conversion may be inaccurate. Consider using '#align finsupp.lsum_single Finsupp.lsum_singleₓ'. -/
theorem lsum_single (f : α → M →ₗ[R] N) (i : α) (m : M) :
Finsupp.lsum S f (Finsupp.single i m) = f i m :=
@@ -670,7 +670,7 @@ noncomputable def lift : (X → M) ≃+ ((X →₀ R) →ₗ[R] M) :=
lean 3 declaration is
forall (M : Type.{u1}) (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u3}) (f : LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (x : X), Eq.{succ u1} M (coeFn.{max (succ (max (max u3 u2) u1)) (succ 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_inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (X -> M) (LinearMap.hasAdd.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R 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but is expected to have type
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Case conversion may be inaccurate. Consider using '#align finsupp.lift_symm_apply Finsupp.lift_symm_applyₓ'. -/
@[simp]
theorem lift_symm_apply (f) (x) : ((lift M R X).symm f) x = f (single x 1) :=
@@ -681,7 +681,7 @@ theorem lift_symm_apply (f) (x) : ((lift M R X).symm f) x = f (single x 1) :=
lean 3 declaration is
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but is expected to have type
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+ forall (M : Type.{u1}) (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u3}) (f : X -> M) (g : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) g) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : X -> M) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (Finsupp.lift.{u1, u2, u3} M R _inst_1 _inst_3 _inst_4 X) f) g) (Finsupp.sum.{u3, u2, u1} X R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) _inst_3 g (fun (x : X) (r : R) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4))))) r (f x)))
Case conversion may be inaccurate. Consider using '#align finsupp.lift_apply Finsupp.lift_applyₓ'. -/
@[simp]
theorem lift_apply (f) (g) : ((lift M R X) f) g = g.Sum fun x r => r • f x :=
@@ -711,7 +711,7 @@ noncomputable def llift : (X → M) ≃ₗ[S] (X →₀ R) →ₗ[R] M :=
lean 3 declaration is
forall (M : Type.{u1}) (R : Type.{u2}) (S : Type.{u3}) [_inst_1 : Semiring.{u2} R] [_inst_2 : Semiring.{u3} S] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u4}) [_inst_9 : Module.{u3, u1} S M _inst_2 _inst_3] [_inst_10 : SMulCommClass.{u2, u3, u1} R S M (SMulZeroClass.toHasSmul.{u2, u1} R M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u1} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u3, u1} S M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u1} S M (MulZeroClass.toHasZero.{u3} S (MulZeroOneClass.toMulZeroClass.{u3} S (MonoidWithZero.toMulZeroOneClass.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)))) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u1} S M (Semiring.toMonoidWithZero.{u3} S _inst_2) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Module.toMulActionWithZero.{u3, u1} S M _inst_2 _inst_3 _inst_9))))] (f : X -> M) (x : Finsupp.{u4, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))), Eq.{succ u1} M (coeFn.{max (succ (max u4 u2)) (succ u1), max (succ (max u4 u2)) (succ u1)} (LinearMap.{u2, u2, max u4 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u4, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u4, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u2, u2, max u4 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u4, u2} X R 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(AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.hasAdd.{u2, u2, max u4 u2, u1} R R (Finsupp.{u4, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.lift.{u1, u2, u4} M R _inst_1 _inst_3 _inst_4 X) f) x)
but is expected to have type
- forall (M : Type.{u2}) (R : Type.{u3}) (S : Type.{u1}) [_inst_1 : Semiring.{u3} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (X : Type.{u4}) [_inst_9 : Module.{u1, u2} S M _inst_2 _inst_3] [_inst_10 : SMulCommClass.{u3, u1, u2} R S M (SMulZeroClass.toSMul.{u3, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u2} R M (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} S M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} S M (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u1, u2} S M _inst_2 _inst_3 _inst_9))))] (f : X -> M) (x : Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) => M) x) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : X -> M) => LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) f) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (fun (_x : Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u2) (succ u4), max (max (succ u2) (succ u3)) (succ u4)} (LinearEquiv.{u1, u1, max u2 u4, max u2 u3 u4} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R 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X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddMonoid.toZero.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u3) u4} S (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddMonoid.toAddZeroClass.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u3) u4} S (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u2 u3) u4} S (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) _inst_2 (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u3 u4, u2} R R S (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u3) u4, u1, max u2 u4, max (max u2 u3) u4} (LinearEquiv.{u1, u1, max u2 u4, max u2 u3 u4} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u4, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u3 u4, u2} R R S (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max u2 u4} (X -> M) (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Module.toDistribMulAction.{u1, max u2 u4} S (X -> M) _inst_2 (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (Pi.module.{u4, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9))) (Module.toDistribMulAction.{u1, max (max u2 u3) u4} S (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R 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(a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5047 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (LinearMap.instAddLinearMap.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (Pi.instAdd.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5047 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (LinearMap.instAddLinearMap.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (AddEquiv.instAddEquivClassAddEquiv.{max u2 u4, max (max u2 u3) u4} (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (Pi.instAdd.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5047 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (LinearMap.instAddLinearMap.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) (Finsupp.lift.{u2, u3, u4} M R _inst_1 _inst_3 _inst_4 X) f) x)
+ forall (M : Type.{u2}) (R : Type.{u3}) (S : Type.{u1}) [_inst_1 : Semiring.{u3} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (X : Type.{u4}) [_inst_9 : Module.{u1, u2} S M _inst_2 _inst_3] [_inst_10 : SMulCommClass.{u3, u1, u2} R S M (SMulZeroClass.toSMul.{u3, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u2} R M (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} S M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} S M (MonoidWithZero.toZero.{u1} S 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R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u3) u4} S (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u2 u3) u4} S (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) _inst_2 (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u3 u4, u2} R R S (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u3) u4, u1, max u2 u4, max (max u2 u3) u4} (LinearEquiv.{u1, u1, max u2 u4, max u2 u3 u4} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u4, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u3 u4, u2} R R S (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max u2 u4} (X -> M) (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Module.toDistribMulAction.{u1, max u2 u4} S (X -> M) _inst_2 (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (Pi.module.{u4, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9))) (Module.toDistribMulAction.{u1, max (max u2 u3) u4} S (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) _inst_2 (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u3 u4, u2} R R S (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max u2 u4, max (max u2 u3) u4, max (max u2 u3) u4} S (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearEquiv.{u1, u1, max u2 u4, max u2 u3 u4} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R 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(Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) (Finsupp.lift.{u2, u3, u4} M R _inst_1 _inst_3 _inst_4 X) f) x)
Case conversion may be inaccurate. Consider using '#align finsupp.llift_apply Finsupp.llift_applyₓ'. -/
@[simp]
theorem llift_apply (f : X → M) (x : X →₀ R) : llift M R S X f x = lift M R X f x :=
@@ -722,7 +722,7 @@ theorem llift_apply (f : X → M) (x : X →₀ R) : llift M R S X f x = lift M
lean 3 declaration is
forall (M : Type.{u1}) (R : Type.{u2}) (S : Type.{u3}) [_inst_1 : Semiring.{u2} R] [_inst_2 : Semiring.{u3} S] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u4}) [_inst_9 : Module.{u3, u1} S M _inst_2 _inst_3] [_inst_10 : SMulCommClass.{u2, u3, u1} R S M (SMulZeroClass.toHasSmul.{u2, u1} R M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u1} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u3, u1} S M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u1} S M (MulZeroClass.toHasZero.{u3} S (MulZeroOneClass.toMulZeroClass.{u3} S (MonoidWithZero.toMulZeroOneClass.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)))) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u1} S M (Semiring.toMonoidWithZero.{u3} S _inst_2) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Module.toMulActionWithZero.{u3, u1} S M _inst_2 _inst_3 _inst_9))))] (f : LinearMap.{u2, u2, max u4 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u4, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u4, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (x : X), Eq.{succ u1} M (coeFn.{max (succ (max (max u4 u2) u1)) (succ (max u4 u1)), max (succ (max (max u4 u2) u1)) (succ (max u4 u1))} (LinearEquiv.{u3, u3, max (max u4 u2) u1, max u4 u1} S S _inst_2 _inst_2 (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2)) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2)) (RingHomInvPair.ids.{u3} S _inst_2) (RingHomInvPair.ids.{u3} S _inst_2) (LinearMap.{u2, u2, max u4 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u4, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u4, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (X -> M) (LinearMap.addCommMonoid.{u2, u2, max u4 u2, u1} R R (Finsupp.{u4, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 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but is expected to have type
- forall (M : Type.{u2}) (R : Type.{u4}) (S : Type.{u1}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] (X : Type.{u3}) [_inst_9 : Module.{u1, u2} S M _inst_2 _inst_3] [_inst_10 : SMulCommClass.{u4, u1, u2} R S M (SMulZeroClass.toSMul.{u4, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u4, u2} R M (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u4, u2} R M (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u4, u2} R M _inst_1 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} S M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} S M (MonoidWithZero.toZero.{u1} S 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) _inst_2 (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u1, max u4 u3, u2} R R S (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (SMulZeroClass.toSMul.{u1, max u2 u3} S (X -> M) (AddMonoid.toZero.{max u2 u3} (X -> M) (AddCommMonoid.toAddMonoid.{max u2 u3} (X -> M) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)))) (DistribSMul.toSMulZeroClass.{u1, max u2 u3} S (X -> M) (AddMonoid.toAddZeroClass.{max u2 u3} (X -> M) (AddCommMonoid.toAddMonoid.{max u2 u3} (X -> M) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)))) (DistribMulAction.toDistribSMul.{u1, max u2 u3} S (X -> M) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max u2 u3} (X -> M) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3))) (Module.toDistribMulAction.{u1, max u2 u3} S (X -> M) _inst_2 (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (Pi.module.{u3, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u4) u3, u1, max (max u2 u4) u3, max u2 u3} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u2 u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (X -> M) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u1, max u4 u3, u2} R R S (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9))) S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (X -> M) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u3} (X -> M) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) _inst_2 (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u1, max u4 u3, u2} R R S (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (Module.toDistribMulAction.{u1, max u2 u3} S (X -> M) _inst_2 (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (Pi.module.{u3, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9))) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u2 u4) u3, max u2 u3, max (max u2 u4) u3} S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (X -> M) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u2 u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (X -> M) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u1, max u4 u3, u2} R R S (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9))) _inst_2 (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u1, max u4 u3, u2} R R S (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9)) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max (max u2 u4) u3, max u2 u3, max (max u2 u4) u3} S S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R 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(Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u1, max u4 u3, u2} R R S (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R 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u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} X (fun (ᾰ : X) => M) (fun (i : X) => _inst_3)) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.module.{u3, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9)) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u1, max u4 u3, u2} R R S (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (Finsupp.llift.{u2, u4, u1, u3} M R S _inst_1 _inst_2 _inst_3 _inst_4 X _inst_9 _inst_10)) f x) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) (fun (_x : Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) f (Finsupp.single.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)) x (OfNat.ofNat.{u4} R 1 (One.toOfNat1.{u4} R (Semiring.toOne.{u4} R _inst_1)))))
+ forall (M : Type.{u2}) (R : Type.{u4}) (S : Type.{u1}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] (X : Type.{u3}) [_inst_9 : Module.{u1, u2} S M _inst_2 _inst_3] [_inst_10 : SMulCommClass.{u4, u1, u2} R S M (SMulZeroClass.toSMul.{u4, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u4, u2} R M (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u4, u2} R M (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u4, u2} R M _inst_1 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} S M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} S M (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u1, u2} S M _inst_2 _inst_3 _inst_9))))] (f : LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (x : X), Eq.{succ u2} M (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u3)} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u2 u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (X -> M) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u1, max u4 u3, u2} R R S (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9))) (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) => X -> M) _x) (SMulHomClass.toFunLike.{max (max u2 u4) u3, u1, max (max u2 u4) u3, max u2 u3} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u2 u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (X -> M) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u1, max u4 u3, u2} R R S (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9))) S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (X -> M) (SMulZeroClass.toSMul.{u1, max (max u2 u4) u3} S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (AddMonoid.toZero.{max (max u2 u4) u3} (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u4) u3} S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (AddMonoid.toAddZeroClass.{max (max u2 u4) u3} (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u4) u3} S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) _inst_2 (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u1, max u4 u3, u2} R R S (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (SMulZeroClass.toSMul.{u1, max u2 u3} S (X -> M) (AddMonoid.toZero.{max u2 u3} (X -> M) (AddCommMonoid.toAddMonoid.{max u2 u3} (X -> M) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)))) (DistribSMul.toSMulZeroClass.{u1, max u2 u3} S (X -> M) (AddMonoid.toAddZeroClass.{max u2 u3} (X -> M) (AddCommMonoid.toAddMonoid.{max u2 u3} (X -> M) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)))) (DistribMulAction.toDistribSMul.{u1, max u2 u3} S (X -> M) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max u2 u3} (X -> M) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3))) (Module.toDistribMulAction.{u1, max u2 u3} S (X -> M) _inst_2 (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (Pi.module.{u3, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u4) u3, u1, max (max u2 u4) u3, max u2 u3} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u2 u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (X -> M) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u1, max u4 u3, u2} R R S (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9))) S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (X -> M) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u3} (X -> M) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) _inst_2 (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u1, max u4 u3, u2} R R S (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (Module.toDistribMulAction.{u1, max u2 u3} S (X -> M) _inst_2 (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (Pi.module.{u3, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9))) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u2 u4) u3, max u2 u3, max (max u2 u4) u3} S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (X -> M) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u2 u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (X -> M) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u1, max u4 u3, u2} R R S (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) 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Case conversion may be inaccurate. Consider using '#align finsupp.llift_symm_apply Finsupp.llift_symm_applyₓ'. -/
@[simp]
theorem llift_symm_apply (f : (X →₀ R) →ₗ[R] M) (x : X) :
@@ -754,7 +754,7 @@ def lmapDomain (f : α → α') : (α →₀ M) →ₗ[R] α' →₀ M
lean 3 declaration is
forall {α : Type.{u1}} (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {α' : Type.{u4}} (f : α -> α') (l : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))), Eq.{max (succ u4) (succ u2)} (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (coeFn.{max (succ (max u1 u2)) (succ (max u4 u2)), max (succ (max u1 u2)) (succ (max u4 u2))} (LinearMap.{u3, u3, max u1 u2, max u4 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4)) (fun (_x : LinearMap.{u3, u3, max u1 u2, max u4 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4)) => (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) -> (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))))) (LinearMap.hasCoeToFun.{u3, u3, max u1 u2, max u4 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lmapDomain.{u1, u2, u3, u4} α M R _inst_1 _inst_3 _inst_4 α' f) l) (Finsupp.mapDomain.{u1, u4, u2} α α' M _inst_3 f l)
but is expected to have type
- forall {α : Type.{u4}} (M : Type.{u3}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u1, u3} R M _inst_1 _inst_3] {α' : Type.{u2}} (f : α -> α') (l : Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) l) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u3), max (succ u3) (succ u2)} (LinearMap.{u1, u1, max u3 u4, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.addCommMonoid.{u4, u3} α M _inst_3) (Finsupp.addCommMonoid.{u2, u3} α' M _inst_3) (Finsupp.module.{u4, u3, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u2, u3, u1} α' M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (fun (_x : Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max u3 u2} R R (Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} α M _inst_3) (Finsupp.addCommMonoid.{u2, u3} α' M _inst_3) (Finsupp.module.{u4, u3, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u2, u3, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lmapDomain.{u4, u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 α' f) l) (Finsupp.mapDomain.{u4, u2, u3} α α' M _inst_3 f l)
+ forall {α : Type.{u4}} (M : Type.{u3}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u1, u3} R M _inst_1 _inst_3] {α' : Type.{u2}} (f : α -> α') (l : Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) l) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u3), max (succ u3) (succ u2)} (LinearMap.{u1, u1, max u3 u4, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.addCommMonoid.{u4, u3} α M _inst_3) (Finsupp.addCommMonoid.{u2, u3} α' M _inst_3) (Finsupp.module.{u4, u3, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u2, u3, u1} α' M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (fun (_x : Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max u3 u2} R R (Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} α M _inst_3) (Finsupp.addCommMonoid.{u2, u3} α' M _inst_3) (Finsupp.module.{u4, u3, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u2, u3, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lmapDomain.{u4, u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 α' f) l) (Finsupp.mapDomain.{u4, u2, u3} α α' M _inst_3 f l)
Case conversion may be inaccurate. Consider using '#align finsupp.lmap_domain_apply Finsupp.lmapDomain_applyₓ'. -/
@[simp]
theorem lmapDomain_apply (f : α → α') (l : α →₀ M) :
@@ -788,7 +788,7 @@ theorem lmapDomain_comp (f : α → α') (g : α' → α'') :
lean 3 declaration is
forall {α : Type.{u1}} (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {α' : Type.{u4}} (f : α -> α') (s : Set.{u4} α'), LE.le.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toHasLe.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))))) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (Set.preimage.{u1, u4} α α' f s)) (Submodule.comap.{u3, u3, max u1 u2, max u4 u2, max (max u1 u2) u4 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, max u1 u2, max u4 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u3, u3, max u1 u2, max u4 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lmapDomain.{u1, u2, u3, u4} α M R _inst_1 _inst_3 _inst_4 α' f) (Finsupp.supported.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4 s))
but is expected to have type
- forall {α : Type.{u3}} (M : Type.{u2}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {α' : Type.{u4}} (f : α -> α') (s : Set.{u4} α'), LE.le.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toLE.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))))) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (Set.preimage.{u3, u4} α α' f s)) (Submodule.comap.{u1, u1, max u3 u2, max u2 u4, max (max u2 u4) u3} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, max u2 u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u1} α' M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u3 u2, max u2 u4} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lmapDomain.{u3, u2, u1, u4} α M R _inst_1 _inst_3 _inst_4 α' f) (Finsupp.supported.{u4, u2, u1} α' M R _inst_1 _inst_3 _inst_4 s))
+ forall {α : Type.{u3}} (M : Type.{u2}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {α' : Type.{u4}} (f : α -> α') (s : Set.{u4} α'), LE.le.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toLE.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))))) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (Set.preimage.{u3, u4} α α' f s)) (Submodule.comap.{u1, u1, max u3 u2, max u2 u4, max (max u2 u4) u3} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, max u2 u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u1} α' M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u1, u1, max u3 u2, max u2 u4} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lmapDomain.{u3, u2, u1, u4} α M R _inst_1 _inst_3 _inst_4 α' f) (Finsupp.supported.{u4, u2, u1} α' M R _inst_1 _inst_3 _inst_4 s))
Case conversion may be inaccurate. Consider using '#align finsupp.supported_comap_lmap_domain Finsupp.supported_comap_lmapDomainₓ'. -/
theorem supported_comap_lmapDomain (f : α → α') (s : Set α') :
supported M R (f ⁻¹' s) ≤ (supported M R s).comap (lmapDomain M R f) :=
@@ -803,7 +803,7 @@ theorem supported_comap_lmapDomain (f : α → α') (s : Set α') :
lean 3 declaration is
forall {α : Type.{u1}} (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {α' : Type.{u4}} [_inst_9 : Nonempty.{succ u1} α] (f : α -> α') (s : Set.{u1} α), Eq.{succ (max u4 u2)} (Submodule.{u3, max u4 u2} R (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4)) (Submodule.map.{u3, u3, max u1 u2, max u4 u2, max (max u1 u2) u4 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomSurjective.ids.{u3} R _inst_1) (LinearMap.{u3, u3, max u1 u2, max u4 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u3, u3, max u1 u2, max u4 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lmapDomain.{u1, u2, u3, u4} α M R _inst_1 _inst_3 _inst_4 α' f) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.supported.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4 (Set.image.{u1, u4} α α' f s))
but is expected to have type
- forall {α : Type.{u4}} (M : Type.{u3}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u1, u3} R M _inst_1 _inst_3] {α' : Type.{u2}} [_inst_9 : Nonempty.{succ u4} α] (f : α -> α') (s : Set.{u4} α), Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u3 u2} R (Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u2, u3} α' M _inst_3) (Finsupp.module.{u2, u3, u1} α' M R _inst_1 _inst_3 _inst_4)) (Submodule.map.{u1, u1, max u4 u3, max u3 u2, max (max u3 u2) u4} R R (Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} α M _inst_3) (Finsupp.addCommMonoid.{u2, u3} α' M _inst_3) (Finsupp.module.{u4, u3, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u2, u3, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.{u1, u1, max u3 u4, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.addCommMonoid.{u4, u3} α M _inst_3) (Finsupp.addCommMonoid.{u2, u3} α' M _inst_3) (Finsupp.module.{u4, u3, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u2, u3, u1} α' M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u4 u3, max u3 u2} R R (Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} α M _inst_3) (Finsupp.addCommMonoid.{u2, u3} α' M _inst_3) (Finsupp.module.{u4, u3, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u2, u3, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lmapDomain.{u4, u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 α' f) (Finsupp.supported.{u4, u3, u1} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.supported.{u2, u3, u1} α' M R _inst_1 _inst_3 _inst_4 (Set.image.{u4, u2} α α' f s))
+ forall {α : Type.{u4}} (M : Type.{u3}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u1, u3} R M _inst_1 _inst_3] {α' : Type.{u2}} [_inst_9 : Nonempty.{succ u4} α] (f : α -> α') (s : Set.{u4} α), Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u3 u2} R (Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u2, u3} α' M _inst_3) (Finsupp.module.{u2, u3, u1} α' M R _inst_1 _inst_3 _inst_4)) (Submodule.map.{u1, u1, max u4 u3, max u3 u2, max (max u3 u2) u4} R R (Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} α M _inst_3) (Finsupp.addCommMonoid.{u2, u3} α' M _inst_3) (Finsupp.module.{u4, u3, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u2, u3, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.{u1, u1, max u3 u4, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.addCommMonoid.{u4, u3} α M _inst_3) (Finsupp.addCommMonoid.{u2, u3} α' M _inst_3) (Finsupp.module.{u4, u3, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u2, u3, u1} α' M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u1, u1, max u4 u3, max u3 u2} R R (Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} α M _inst_3) (Finsupp.addCommMonoid.{u2, u3} α' M _inst_3) (Finsupp.module.{u4, u3, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u2, u3, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lmapDomain.{u4, u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 α' f) (Finsupp.supported.{u4, u3, u1} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.supported.{u2, u3, u1} α' M R _inst_1 _inst_3 _inst_4 (Set.image.{u4, u2} α α' f s))
Case conversion may be inaccurate. Consider using '#align finsupp.lmap_domain_supported Finsupp.lmapDomain_supportedₓ'. -/
theorem lmapDomain_supported [Nonempty α] (f : α → α') (s : Set α) :
(supported M R s).map (lmapDomain M R f) = supported M R (f '' s) :=
@@ -828,7 +828,7 @@ theorem lmapDomain_supported [Nonempty α] (f : α → α') (s : Set α) :
lean 3 declaration is
forall {α : Type.{u1}} (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {α' : Type.{u4}} (f : α -> α') {s : Set.{u1} α}, (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (Eq.{succ u4} α' (f a) (f b)) -> (Eq.{succ u1} α a b))) -> (Disjoint.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) (Submodule.orderBot.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s) (LinearMap.ker.{u3, u3, max u1 u2, max u4 u2, max (max u1 u2) u4 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, max u1 u2, max u4 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u3, u3, max u1 u2, max u4 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lmapDomain.{u1, u2, u3, u4} α M R _inst_1 _inst_3 _inst_4 α' f)))
but is expected to have type
- forall {α : Type.{u4}} (M : Type.{u2}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {α' : Type.{u3}} (f : α -> α') {s : Set.{u4} α}, (forall (a : α), (Membership.mem.{u4, u4} α (Set.{u4} α) (Set.instMembershipSet.{u4} α) a s) -> (forall (b : α), (Membership.mem.{u4, u4} α (Set.{u4} α) (Set.instMembershipSet.{u4} α) b s) -> (Eq.{succ u3} α' (f a) (f b)) -> (Eq.{succ u4} α a b))) -> (Disjoint.{max u2 u4} (Submodule.{u1, max u2 u4} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u4 u2} (Submodule.{u1, max u2 u4} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u4 u2} (Submodule.{u1, max u2 u4} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u4 u2} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u1, max u4 u2} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) (LinearMap.ker.{u1, u1, max u4 u2, max u2 u3, max (max u2 u3) u4} R R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u4, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α' M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u4 u2, max u2 u3} R R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lmapDomain.{u4, u2, u1, u3} α M R _inst_1 _inst_3 _inst_4 α' f)))
+ forall {α : Type.{u4}} (M : Type.{u2}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {α' : Type.{u3}} (f : α -> α') {s : Set.{u4} α}, (forall (a : α), (Membership.mem.{u4, u4} α (Set.{u4} α) (Set.instMembershipSet.{u4} α) a s) -> (forall (b : α), (Membership.mem.{u4, u4} α (Set.{u4} α) (Set.instMembershipSet.{u4} α) b s) -> (Eq.{succ u3} α' (f a) (f b)) -> (Eq.{succ u4} α a b))) -> (Disjoint.{max u2 u4} (Submodule.{u1, max u2 u4} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u4 u2} (Submodule.{u1, max u2 u4} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u4 u2} (Submodule.{u1, max u2 u4} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u4 u2} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u1, max u4 u2} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) (LinearMap.ker.{u1, u1, max u4 u2, max u2 u3, max (max u2 u3) u4} R R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u4, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α' M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u1, u1, max u4 u2, max u2 u3} R R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lmapDomain.{u4, u2, u1, u3} α M R _inst_1 _inst_3 _inst_4 α' f)))
Case conversion may be inaccurate. Consider using '#align finsupp.lmap_domain_disjoint_ker Finsupp.lmapDomain_disjoint_kerₓ'. -/
/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a b «expr ∈ » s) -/
theorem lmapDomain_disjoint_ker (f : α → α') {s : Set α}
@@ -907,7 +907,7 @@ variable {α M v}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {v : α -> M} (l : Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v) l) (Finsupp.sum.{u1, u3, u2} α R M (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 l (fun (i : α) (a : R) => SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) a (v i)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {v : α -> M} (l : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 v) l) (Finsupp.sum.{u3, u2, u1} α R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) _inst_3 l (fun (i : α) (a : R) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4))))) a (v i)))
+ forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {v : α -> M} (l : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 v) l) (Finsupp.sum.{u3, u2, u1} α R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) _inst_3 l (fun (i : α) (a : R) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4))))) a (v i)))
Case conversion may be inaccurate. Consider using '#align finsupp.total_apply Finsupp.total_applyₓ'. -/
theorem total_apply (l : α →₀ R) : Finsupp.total α M R v l = l.Sum fun i a => a • v i :=
rfl
@@ -917,7 +917,7 @@ theorem total_apply (l : α →₀ R) : Finsupp.total α M R v l = l.Sum fun i a
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {v : α -> M} {l : Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))} {s : Finset.{u1} α}, (Membership.Mem.{max u1 u3, max u1 u3} (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (SetLike.hasMem.{max u1 u3, max u1 u3} (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) (Submodule.setLike.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)))) l (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} α) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (Finset.Set.hasCoeT.{u1} α))) s))) -> (Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v) l) (Finset.sum.{u2, u1} M α _inst_3 s (fun (i : α) => SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (fun (_x : Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) => α -> R) (Finsupp.coeFun.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) l i) (v i))))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {v : α -> M} {l : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))} {s : Finset.{u3} α}, (Membership.mem.{max u3 u2, max u2 u3} (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (Submodule.setLike.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)))) l (Finsupp.supported.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1) (Finset.toSet.{u3} α s))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 v) l) (Finset.sum.{u1, u3} M α _inst_3 s (fun (i : α) => HSMul.hSMul.{u2, u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M M (instHSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (SMulZeroClass.toSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M _inst_1 _inst_3 _inst_4))))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) α (fun (_x : α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) _x) (Finsupp.funLike.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) l i) (v i))))
+ forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {v : α -> M} {l : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))} {s : Finset.{u3} α}, (Membership.mem.{max u3 u2, max u2 u3} (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (Submodule.setLike.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)))) l (Finsupp.supported.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1) (Finset.toSet.{u3} α s))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 v) l) (Finset.sum.{u1, u3} M α _inst_3 s (fun (i : α) => HSMul.hSMul.{u2, u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M M (instHSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (SMulZeroClass.toSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M _inst_1 _inst_3 _inst_4))))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) α (fun (_x : α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) _x) (Finsupp.funLike.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) l i) (v i))))
Case conversion may be inaccurate. Consider using '#align finsupp.total_apply_of_mem_supported Finsupp.total_apply_of_mem_supportedₓ'. -/
theorem total_apply_of_mem_supported {l : α →₀ R} {s : Finset α}
(hs : l ∈ supported R R (↑s : Set α)) : Finsupp.total α M R v l = s.Sum fun i => l i • v i :=
@@ -929,7 +929,7 @@ theorem total_apply_of_mem_supported {l : α →₀ R} {s : Finset α}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {v : α -> M} (c : R) (a : α), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v) (Finsupp.single.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) a c)) (SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) c (v a))
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u3}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u1, u3} R M _inst_1 _inst_3] {v : α -> M} (c : R) (a : α), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) (Finsupp.single.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) a c)) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u1), succ u3} (LinearMap.{u1, u1, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u3} R R (Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4 v) (Finsupp.single.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) a c)) (HSMul.hSMul.{u1, u3, u3} R M M (instHSMul.{u1, u3} R M (SMulZeroClass.toSMul.{u1, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u1, u3} R M _inst_1 _inst_3 _inst_4))))) c (v a))
+ forall {α : Type.{u2}} {M : Type.{u3}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u1, u3} R M _inst_1 _inst_3] {v : α -> M} (c : R) (a : α), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) (Finsupp.single.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) a c)) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u1), succ u3} (LinearMap.{u1, u1, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u3} R R (Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4 v) (Finsupp.single.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) a c)) (HSMul.hSMul.{u1, u3, u3} R M M (instHSMul.{u1, u3} R M (SMulZeroClass.toSMul.{u1, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u1, u3} R M _inst_1 _inst_3 _inst_4))))) c (v a))
Case conversion may be inaccurate. Consider using '#align finsupp.total_single Finsupp.total_singleₓ'. -/
@[simp]
theorem total_single (c : R) (a : α) : Finsupp.total α M R v (single a c) = c • v a := by
@@ -940,7 +940,7 @@ theorem total_single (c : R) (a : α) : Finsupp.total α M R v (single a c) = c
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (x : Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u1 u2} (α -> M) 0 (OfNat.mk.{max u1 u2} (α -> M) 0 (Zero.zero.{max u1 u2} (α -> M) (Pi.instZero.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))))))) x) (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))))))
but is expected to have type
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+ forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u3 u1} (α -> M) 0 (Zero.toOfNat0.{max u3 u1} (α -> M) (Pi.instZero.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.6886 : α) => M) (fun (i : α) => AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) _inst_3))))
Case conversion may be inaccurate. Consider using '#align finsupp.total_zero_apply Finsupp.total_zero_applyₓ'. -/
theorem total_zero_apply (x : α →₀ R) : (Finsupp.total α M R 0) x = 0 := by
simp [Finsupp.total_apply]
@@ -965,7 +965,7 @@ variable {α M}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {M' : Type.{u4}} [_inst_9 : AddCommMonoid.{u4} M'] [_inst_10 : Module.{u3, u4} R M' _inst_1 _inst_9] (f : LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_3 _inst_9 _inst_4 _inst_10) (v : α -> M) (l : Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))), Eq.{succ u4} M' (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_3 _inst_9 _inst_4 _inst_10) (fun (_x : LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' 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(x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, u2} R R M _inst_1 _inst_3 _inst_3 M' _inst_4 _inst_10 _inst_9 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_3))) f) v)) l)
Case conversion may be inaccurate. Consider using '#align finsupp.apply_total Finsupp.apply_totalₓ'. -/
theorem apply_total (f : M →ₗ[R] M') (v) (l : α →₀ R) :
f (Finsupp.total α M R v l) = Finsupp.total α M' R (f ∘ v) l := by
@@ -976,7 +976,7 @@ theorem apply_total (f : M →ₗ[R] M') (v) (l : α →₀ R) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] [_inst_11 : Unique.{succ u1} α] (l : Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (v : α -> M), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v) l) (SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (fun (_x : Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) => α -> R) (Finsupp.coeFun.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) l (Inhabited.default.{succ u1} α (Unique.inhabited.{succ u1} α _inst_11))) (v (Inhabited.default.{succ u1} α (Unique.inhabited.{succ u1} α _inst_11))))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] [_inst_11 : Unique.{succ u3} α] (l : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (v : α -> M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 v) l) (HSMul.hSMul.{u2, u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M M (instHSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M (SMulZeroClass.toSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M _inst_1 _inst_3 _inst_4))))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) α (fun (_x : α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) _x) (Finsupp.funLike.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) l (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) (v (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))))
+ forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] [_inst_11 : Unique.{succ u3} α] (l : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (v : α -> M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 v) l) (HSMul.hSMul.{u2, u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M M (instHSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M (SMulZeroClass.toSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M _inst_1 _inst_3 _inst_4))))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) α (fun (_x : α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) _x) (Finsupp.funLike.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) l (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) (v (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))))
Case conversion may be inaccurate. Consider using '#align finsupp.total_unique Finsupp.total_uniqueₓ'. -/
theorem total_unique [Unique α] (l : α →₀ R) (v) :
Finsupp.total α M R v l = l default • v default := by rw [← total_single, ← unique_single l]
@@ -986,7 +986,7 @@ theorem total_unique [Unique α] (l : α →₀ R) (v) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {v : α -> M}, (Function.Surjective.{succ u1, succ u2} α M v) -> (Function.Surjective.{max (succ u1) (succ u3), succ u2} (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {v : α -> M}, (Function.Surjective.{succ u3, succ u2} α M v) -> (Function.Surjective.{max (succ u3) (succ u1), succ u2} (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u1), succ u2} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 v)))
+ forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {v : α -> M}, (Function.Surjective.{succ u3, succ u2} α M v) -> (Function.Surjective.{max (succ u3) (succ u1), succ u2} (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u1), succ u2} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 v)))
Case conversion may be inaccurate. Consider using '#align finsupp.total_surjective Finsupp.total_surjectiveₓ'. -/
theorem total_surjective (h : Function.Surjective v) :
Function.Surjective (Finsupp.total α M R v) :=
@@ -1000,7 +1000,7 @@ theorem total_surjective (h : Function.Surjective v) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {v : α -> M}, (Function.Surjective.{succ u1, succ u2} α M v) -> (Eq.{succ u2} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) (LinearMap.range.{u3, u3, max u1 u3, u2, max (max u1 u3) u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.semilinearMapClass.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R _inst_1) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v)) (Top.top.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasTop.{u3, u2} R M _inst_1 _inst_3 _inst_4)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {v : α -> M}, (Function.Surjective.{succ u3, succ u2} α M v) -> (Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (LinearMap.range.{u1, u1, max u3 u1, u2, max (max u3 u2) u1} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 v)) (Top.top.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instTopSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)))
+ forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {v : α -> M}, (Function.Surjective.{succ u3, succ u2} α M v) -> (Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (LinearMap.range.{u1, u1, max u3 u1, u2, max (max u3 u2) u1} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (LinearMap.semilinearMapClass.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 v)) (Top.top.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instTopSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)))
Case conversion may be inaccurate. Consider using '#align finsupp.total_range Finsupp.total_rangeₓ'. -/
theorem total_range (h : Function.Surjective v) : (Finsupp.total α M R v).range = ⊤ :=
range_eq_top.2 <| total_surjective R h
@@ -1010,7 +1010,7 @@ theorem total_range (h : Function.Surjective v) : (Finsupp.total α M R v).range
lean 3 declaration is
forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] (M : Type.{u2}) [_inst_11 : AddCommMonoid.{u2} M] [_inst_12 : Module.{u1, u2} R M _inst_1 _inst_11], Function.Surjective.{max (succ u2) (succ u1), succ u2} (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (coeFn.{max (succ (max u2 u1)) (succ u2), max (succ (max u2 u1)) (succ u2)} (LinearMap.{u1, u1, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_11 (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_12) (fun (_x : LinearMap.{u1, u1, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_11 (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_12) => (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u2} R R (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_11 (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_12 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} M M R _inst_1 _inst_11 _inst_12 (id.{succ u2} M)))
but is expected to have type
- forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] (M : Type.{u2}) [_inst_11 : AddCommMonoid.{u2} M] [_inst_12 : Module.{u1, u2} R M _inst_1 _inst_11], Function.Surjective.{max (succ u1) (succ u2), succ u2} (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_11 (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_12) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u2} R R (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_11 (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_12 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} M M R _inst_1 _inst_11 _inst_12 (id.{succ u2} M)))
+ forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] (M : Type.{u2}) [_inst_11 : AddCommMonoid.{u2} M] [_inst_12 : Module.{u1, u2} R M _inst_1 _inst_11], Function.Surjective.{max (succ u1) (succ u2), succ u2} (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_11 (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_12) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u2} R R (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_11 (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_12 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} M M R _inst_1 _inst_11 _inst_12 (id.{succ u2} M)))
Case conversion may be inaccurate. Consider using '#align finsupp.total_id_surjective Finsupp.total_id_surjectiveₓ'. -/
/-- Any module is a quotient of a free module. This is stated as surjectivity of
`finsupp.total M M R id : (M →₀ R) →ₗ[R] M`. -/
@@ -1023,7 +1023,7 @@ theorem total_id_surjective (M) [AddCommMonoid M] [Module R M] :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {v : α -> M}, Eq.{succ u2} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) (LinearMap.range.{u3, u3, max u1 u3, u2, max (max u1 u3) u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.semilinearMapClass.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R _inst_1) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v)) (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.range.{u2, succ u1} M α v))
but is expected to have type
- forall {α : Type.{u1}} {M : Type.{u3}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_1 _inst_3] {v : α -> M}, Eq.{succ u3} (Submodule.{u2, u3} R M _inst_1 _inst_3 _inst_4) (LinearMap.range.{u2, u2, max u1 u2, u3, max (max u1 u3) u2} R R (Finsupp.{u1, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, max u2 u1, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, max u1 u2, u3} R R (Finsupp.{u1, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R _inst_1) (Finsupp.total.{u1, u3, u2} α M R _inst_1 _inst_3 _inst_4 v)) (Submodule.span.{u2, u3} R M _inst_1 _inst_3 _inst_4 (Set.range.{u3, succ u1} M α v))
+ forall {α : Type.{u1}} {M : Type.{u3}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_1 _inst_3] {v : α -> M}, Eq.{succ u3} (Submodule.{u2, u3} R M _inst_1 _inst_3 _inst_4) (LinearMap.range.{u2, u2, max u1 u2, u3, max (max u1 u3) u2} R R (Finsupp.{u1, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, max u2 u1, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.semilinearMapClass.{u2, u2, max u1 u2, u3} R R (Finsupp.{u1, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R _inst_1) (Finsupp.total.{u1, u3, u2} α M R _inst_1 _inst_3 _inst_4 v)) (Submodule.span.{u2, u3} R M _inst_1 _inst_3 _inst_4 (Set.range.{u3, succ u1} M α v))
Case conversion may be inaccurate. Consider using '#align finsupp.range_total Finsupp.range_totalₓ'. -/
theorem range_total : (Finsupp.total α M R v).range = span R (range v) :=
by
@@ -1047,7 +1047,7 @@ theorem range_total : (Finsupp.total α M R v).range = span R (range v) :=
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {α' : Type.{u4}} {M' : Type.{u5}} [_inst_9 : AddCommMonoid.{u5} M'] [_inst_10 : Module.{u3, u5} R M' _inst_1 _inst_9] {v : α -> M} {v' : α' -> M'} (f : α -> α') (g : LinearMap.{u3, u3, u2, u5} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_3 _inst_9 _inst_4 _inst_10), (forall (i : α), Eq.{succ u5} M' (coeFn.{max (succ u2) (succ u5), max (succ u2) (succ u5)} (LinearMap.{u3, u3, u2, u5} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_3 _inst_9 _inst_4 _inst_10) (fun (_x : LinearMap.{u3, u3, u2, u5} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_3 _inst_9 _inst_4 _inst_10) => M -> M') (LinearMap.hasCoeToFun.{u3, u3, u2, u5} R R M M' _inst_1 _inst_1 _inst_3 _inst_9 _inst_4 _inst_10 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) g (v i)) (v' (f i))) -> (Eq.{max (succ (max u1 u3)) (succ u5)} (LinearMap.{u3, u3, max u1 u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) M' (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_10) (LinearMap.comp.{u3, u3, u3, max u1 u3, max u4 u3, u5} R R R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) (Finsupp.{u4, u3} α' R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M' _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.addCommMonoid.{u4, u3} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Finsupp.module.{u4, u3, u3} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_10 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomCompTriple.right_ids.{u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u4, u5, u3} α' M' R _inst_1 _inst_9 _inst_10 v') (Finsupp.lmapDomain.{u1, u3, u3, u4} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) α' f)) (LinearMap.comp.{u3, u3, u3, max u1 u3, u2, u5} R R R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) M M' _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 _inst_9 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 _inst_10 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomCompTriple.right_ids.{u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) g (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v)))
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u4}} (R : Type.{u5}) {_inst_1 : Type.{u1}} {_inst_3 : Type.{u3}} [_inst_4 : Semiring.{u5} R] [α' : AddCommMonoid.{u3} _inst_3] [M' : AddCommMonoid.{u4} M] [_inst_9 : Module.{u5, u3} R _inst_3 _inst_4 α'] [_inst_10 : Module.{u5, u4} R M _inst_4 M'] {v : α -> M} {v' : _inst_1 -> _inst_3} (f : α -> _inst_1) (g : LinearMap.{u5, u5, u4, u3} R R _inst_4 _inst_4 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) M _inst_3 M' α' _inst_10 _inst_9), (forall (i : α), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => _inst_3) (v i)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_4 _inst_4 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) M _inst_3 M' α' _inst_10 _inst_9) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M _inst_3 _inst_4 _inst_4 M' α' _inst_10 _inst_9 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) g (v i)) (v' (f i))) -> (Eq.{max (max (succ u2) (succ u5)) (succ u3)} (LinearMap.{u5, u5, max u5 u2, u3} R R _inst_4 _inst_4 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (Finsupp.{u2, u5} α R (AddMonoid.toZero.{u5} R (AddCommMonoid.toAddMonoid.{u5} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))))) _inst_3 (Finsupp.addCommMonoid.{u2, u5} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))) α' (Finsupp.module.{u2, u5, u5} α R R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Semiring.toModule.{u5} R _inst_4)) _inst_9) (LinearMap.comp.{u5, u5, u5, max u5 u2, max u5 u1, u3} R R R (Finsupp.{u2, u5} α R (AddMonoid.toZero.{u5} R (AddCommMonoid.toAddMonoid.{u5} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))))) (Finsupp.{u1, u5} _inst_1 R (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_4))) _inst_3 _inst_4 _inst_4 _inst_4 (Finsupp.addCommMonoid.{u2, u5} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))) (Finsupp.addCommMonoid.{u1, u5} _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))) α' (Finsupp.module.{u2, u5, u5} α R R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Semiring.toModule.{u5} R _inst_4)) (Finsupp.module.{u1, u5, u5} _inst_1 R R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Semiring.toModule.{u5} R _inst_4)) _inst_9 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHomCompTriple.ids.{u5, u5} R R _inst_4 _inst_4 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Finsupp.total.{u1, u3, u5} _inst_1 _inst_3 R _inst_4 α' _inst_9 v') (Finsupp.lmapDomain.{u2, u5, u5, u1} α R R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Semiring.toModule.{u5} R _inst_4) _inst_1 f)) (LinearMap.comp.{u5, u5, u5, max u2 u5, u4, u3} R R R (Finsupp.{u2, u5} α R (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_4))) M _inst_3 _inst_4 _inst_4 _inst_4 (Finsupp.addCommMonoid.{u2, u5} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))) M' α' (Finsupp.module.{u2, u5, u5} α R R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Semiring.toModule.{u5} R _inst_4)) _inst_10 _inst_9 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHomCompTriple.ids.{u5, u5} R R _inst_4 _inst_4 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) g (Finsupp.total.{u2, u4, u5} α M R _inst_4 M' _inst_10 v)))
+ forall {α : Type.{u2}} {M : Type.{u4}} (R : Type.{u5}) {_inst_1 : Type.{u1}} {_inst_3 : Type.{u3}} [_inst_4 : Semiring.{u5} R] [α' : AddCommMonoid.{u3} _inst_3] [M' : AddCommMonoid.{u4} M] [_inst_9 : Module.{u5, u3} R _inst_3 _inst_4 α'] [_inst_10 : Module.{u5, u4} R M _inst_4 M'] {v : α -> M} {v' : _inst_1 -> _inst_3} (f : α -> _inst_1) (g : LinearMap.{u5, u5, u4, u3} R R _inst_4 _inst_4 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) M _inst_3 M' α' _inst_10 _inst_9), (forall (i : α), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => _inst_3) (v i)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_4 _inst_4 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) M _inst_3 M' α' _inst_10 _inst_9) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M _inst_3 _inst_4 _inst_4 M' α' _inst_10 _inst_9 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) g (v i)) (v' (f i))) -> (Eq.{max (max (succ u2) (succ u5)) (succ u3)} (LinearMap.{u5, u5, max u5 u2, u3} R R _inst_4 _inst_4 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (Finsupp.{u2, u5} α R (AddMonoid.toZero.{u5} R (AddCommMonoid.toAddMonoid.{u5} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))))) _inst_3 (Finsupp.addCommMonoid.{u2, u5} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))) α' (Finsupp.module.{u2, u5, u5} α R R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Semiring.toModule.{u5} R _inst_4)) _inst_9) (LinearMap.comp.{u5, u5, u5, max u5 u2, max u5 u1, u3} R R R (Finsupp.{u2, u5} α R (AddMonoid.toZero.{u5} R (AddCommMonoid.toAddMonoid.{u5} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))))) (Finsupp.{u1, u5} _inst_1 R (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_4))) _inst_3 _inst_4 _inst_4 _inst_4 (Finsupp.addCommMonoid.{u2, u5} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))) (Finsupp.addCommMonoid.{u1, u5} _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))) α' (Finsupp.module.{u2, u5, u5} α R R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Semiring.toModule.{u5} R _inst_4)) (Finsupp.module.{u1, u5, u5} _inst_1 R R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Semiring.toModule.{u5} R _inst_4)) _inst_9 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHomCompTriple.ids.{u5, u5} R R _inst_4 _inst_4 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Finsupp.total.{u1, u3, u5} _inst_1 _inst_3 R _inst_4 α' _inst_9 v') (Finsupp.lmapDomain.{u2, u5, u5, u1} α R R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Semiring.toModule.{u5} R _inst_4) _inst_1 f)) (LinearMap.comp.{u5, u5, u5, max u2 u5, u4, u3} R R R (Finsupp.{u2, u5} α R (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_4))) M _inst_3 _inst_4 _inst_4 _inst_4 (Finsupp.addCommMonoid.{u2, u5} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))) M' α' (Finsupp.module.{u2, u5, u5} α R R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Semiring.toModule.{u5} R _inst_4)) _inst_10 _inst_9 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHomCompTriple.ids.{u5, u5} R R _inst_4 _inst_4 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) g (Finsupp.total.{u2, u4, u5} α M R _inst_4 M' _inst_10 v)))
Case conversion may be inaccurate. Consider using '#align finsupp.lmap_domain_total Finsupp.lmapDomain_totalₓ'. -/
theorem lmapDomain_total (f : α → α') (g : M →ₗ[R] M') (h : ∀ i, g (v i) = v' (f i)) :
(Finsupp.total α' M' R v').comp (lmapDomain R R f) = g.comp (Finsupp.total α M R v) := by
@@ -1071,7 +1071,7 @@ theorem total_comp_lmapDomain (f : α → α') :
lean 3 declaration is
forall {α : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] {α' : Type.{u3}} {M' : Type.{u4}} [_inst_9 : AddCommMonoid.{u4} M'] [_inst_10 : Module.{u2, u4} R M' _inst_1 _inst_9] {v' : α' -> M'} (f : Function.Embedding.{succ u1, succ u3} α α') (l : Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))), Eq.{succ u4} M' (coeFn.{max (succ (max u3 u2)) (succ u4), max (succ (max u3 u2)) (succ u4)} (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) (fun (_x : LinearMap.{u2, u2, max u3 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) => (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M') (LinearMap.hasCoeToFun.{u2, u2, max u3 u2, u4} R R (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u4, u2} α' M' R _inst_1 _inst_9 _inst_10 v') (Finsupp.embDomain.{u1, u3, u2} α α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) f l)) (coeFn.{max (succ (max u1 u2)) (succ u4), max (succ (max u1 u2)) (succ u4)} (LinearMap.{u2, u2, max u1 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) (fun (_x : LinearMap.{u2, u2, max u1 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) => (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M') (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u4} R R (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u1, u4, u2} α M' R _inst_1 _inst_9 _inst_10 (Function.comp.{succ u1, succ u3, succ u4} α α' M' v' (coeFn.{max 1 (succ u1) (succ u3), max (succ u1) (succ u3)} (Function.Embedding.{succ u1, succ u3} α α') (fun (_x : Function.Embedding.{succ u1, succ u3} α α') => α -> α') (Function.Embedding.hasCoeToFun.{succ u1, succ u3} α α') f))) l)
but is expected to have type
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+ forall {α : Type.{u4}} (R : Type.{u2}) {_inst_1 : Type.{u3}} {α' : Type.{u1}} [M' : Semiring.{u2} R] [_inst_9 : AddCommMonoid.{u1} α'] [_inst_10 : Module.{u2, u1} R α' M' _inst_9] {v' : _inst_1 -> α'} (f : Function.Embedding.{succ u4, succ u3} α _inst_1) (l : Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) => α') (Finsupp.embDomain.{u4, u3, u2} α _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M')) f l)) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R M' M' (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')) (Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) α' (Finsupp.addCommMonoid.{u3, u2} _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')))) _inst_9 (Finsupp.module.{u3, u2, u2} _inst_1 R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Semiring.toModule.{u2} R M')) _inst_10) (Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) (fun (_x : Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) => α') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) α' M' M' (Finsupp.addCommMonoid.{u3, u2} _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')))) _inst_9 (Finsupp.module.{u3, u2, u2} _inst_1 R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Semiring.toModule.{u2} R M')) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Finsupp.total.{u3, u1, u2} _inst_1 α' R M' _inst_9 _inst_10 v') (Finsupp.embDomain.{u4, u3, u2} α _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M')) f l)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u1), max (succ u4) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u4, u1} R R M' M' (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) α' (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')))) _inst_9 (Finsupp.module.{u4, u2, u2} α R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Semiring.toModule.{u2} R M')) _inst_10) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) (fun (_x : Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) => α') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u1} R R (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) α' M' M' (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')))) _inst_9 (Finsupp.module.{u4, u2, u2} α R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Semiring.toModule.{u2} R M')) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Finsupp.total.{u4, u1, u2} α α' R M' _inst_9 _inst_10 (Function.comp.{succ u4, succ u3, succ u1} α _inst_1 α' v' (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Function.Embedding.{succ u4, succ u3} α _inst_1) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => _inst_1) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u3), succ u4, succ u3} (Function.Embedding.{succ u4, succ u3} α _inst_1) α _inst_1 (Function.instEmbeddingLikeEmbedding.{succ u4, succ u3} α _inst_1)) f))) l)
Case conversion may be inaccurate. Consider using '#align finsupp.total_emb_domain Finsupp.total_embDomainₓ'. -/
@[simp]
theorem total_embDomain (f : α ↪ α') (l : α →₀ R) :
@@ -1083,7 +1083,7 @@ theorem total_embDomain (f : α ↪ α') (l : α →₀ R) :
lean 3 declaration is
forall {α : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] {α' : Type.{u3}} {M' : Type.{u4}} [_inst_9 : AddCommMonoid.{u4} M'] [_inst_10 : Module.{u2, u4} R M' _inst_1 _inst_9] {v' : α' -> M'} (f : α -> α') (l : Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))), Eq.{succ u4} M' (coeFn.{max (succ (max u3 u2)) (succ u4), max (succ (max u3 u2)) (succ u4)} (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) (fun (_x : LinearMap.{u2, u2, max u3 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) => (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M') (LinearMap.hasCoeToFun.{u2, u2, max u3 u2, u4} R R (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u4, u2} α' M' R _inst_1 _inst_9 _inst_10 v') (Finsupp.mapDomain.{u1, u3, u2} α α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f l)) (coeFn.{max (succ (max u1 u2)) (succ u4), max (succ (max u1 u2)) (succ u4)} (LinearMap.{u2, u2, max u1 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) (fun (_x : LinearMap.{u2, u2, max u1 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) => (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M') (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u4} R R (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u1, u4, u2} α M' R _inst_1 _inst_9 _inst_10 (Function.comp.{succ u1, succ u3, succ u4} α α' M' v' f)) l)
but is expected to have type
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+ forall {α : Type.{u4}} (R : Type.{u3}) {_inst_1 : Type.{u1}} {α' : Type.{u2}} [M' : Semiring.{u3} R] [_inst_9 : AddCommMonoid.{u2} α'] [_inst_10 : Module.{u3, u2} R α' M' _inst_9] {v' : _inst_1 -> α'} (f : α -> _inst_1) (l : Finsupp.{u4, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u1, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) => α') (Finsupp.mapDomain.{u4, u1, u3} α _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) f l)) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u1), succ u2} (LinearMap.{u3, u3, max u3 u1, u2} R R M' M' (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')) (Finsupp.{u1, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) α' (Finsupp.addCommMonoid.{u1, u3} _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')))) _inst_9 (Finsupp.module.{u1, u3, u3} _inst_1 R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) (Semiring.toModule.{u3} R M')) _inst_10) (Finsupp.{u1, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) (fun (_x : Finsupp.{u1, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u1, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) => α') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u1, u2} R R (Finsupp.{u1, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) α' M' M' (Finsupp.addCommMonoid.{u1, u3} _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')))) _inst_9 (Finsupp.module.{u1, u3, u3} _inst_1 R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) (Semiring.toModule.{u3} R M')) _inst_10 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) (Finsupp.total.{u1, u2, u3} _inst_1 α' R M' _inst_9 _inst_10 v') (Finsupp.mapDomain.{u4, u1, u3} α _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) f l)) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} R R M' M' (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')) (Finsupp.{u4, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) α' (Finsupp.addCommMonoid.{u4, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')))) _inst_9 (Finsupp.module.{u4, u3, u3} α R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) (Semiring.toModule.{u3} R M')) _inst_10) (Finsupp.{u4, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) (fun (_x : Finsupp.{u4, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u4, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) => α') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} R R (Finsupp.{u4, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) α' M' M' (Finsupp.addCommMonoid.{u4, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')))) _inst_9 (Finsupp.module.{u4, u3, u3} α R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) (Semiring.toModule.{u3} R M')) _inst_10 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) (Finsupp.total.{u4, u2, u3} α α' R M' _inst_9 _inst_10 (Function.comp.{succ u4, succ u1, succ u2} α _inst_1 α' v' f)) l)
Case conversion may be inaccurate. Consider using '#align finsupp.total_map_domain Finsupp.total_mapDomainₓ'. -/
@[simp]
theorem total_mapDomain (f : α → α') (l : α →₀ R) :
@@ -1095,7 +1095,7 @@ theorem total_mapDomain (f : α → α') (l : α →₀ R) :
lean 3 declaration is
forall {α : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] {α' : Type.{u3}} {M' : Type.{u4}} [_inst_9 : AddCommMonoid.{u4} M'] [_inst_10 : Module.{u2, u4} R M' _inst_1 _inst_9] {v' : α' -> M'} (f : Equiv.{succ u1, succ u3} α α') (l : Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))), Eq.{succ u4} M' (coeFn.{max (succ (max u3 u2)) (succ u4), max (succ (max u3 u2)) (succ u4)} (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) (fun (_x : LinearMap.{u2, u2, max u3 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) => (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M') (LinearMap.hasCoeToFun.{u2, u2, max u3 u2, u4} R R (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u4, u2} α' M' R _inst_1 _inst_9 _inst_10 v') (Finsupp.equivMapDomain.{u1, u3, u2} α α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) f l)) (coeFn.{max (succ (max u1 u2)) (succ u4), max (succ (max u1 u2)) (succ u4)} (LinearMap.{u2, u2, max u1 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) (fun (_x : LinearMap.{u2, u2, max u1 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) => (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M') (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u4} R R (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u1, u4, u2} α M' R _inst_1 _inst_9 _inst_10 (Function.comp.{succ u1, succ u3, succ u4} α α' M' v' (coeFn.{max 1 (max (succ u1) (succ u3)) (succ u3) (succ u1), max (succ u1) (succ u3)} (Equiv.{succ u1, succ u3} α α') (fun (_x : Equiv.{succ u1, succ u3} α α') => α -> α') (Equiv.hasCoeToFun.{succ u1, succ u3} α α') f))) l)
but is expected to have type
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Case conversion may be inaccurate. Consider using '#align finsupp.total_equiv_map_domain Finsupp.total_equivMapDomainₓ'. -/
@[simp]
theorem total_equivMapDomain (f : α ≃ α') (l : α →₀ R) :
@@ -1107,7 +1107,7 @@ theorem total_equivMapDomain (f : α ≃ α') (l : α →₀ R) :
lean 3 declaration is
forall {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (s : Set.{u1} M), Eq.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.span.{u2, u1} R M _inst_1 _inst_3 _inst_4 s) (LinearMap.range.{u2, u2, max u1 u2, u1, max u1 u2} R R (Finsupp.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} M) Type.{u1} (Set.hasCoeToSort.{u1} M) s) R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} M) Type.{u1} (Set.hasCoeToSort.{u1} M) s) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u2, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} M) Type.{u1} (Set.hasCoeToSort.{u1} M) s) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, max u1 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} M) Type.{u1} (Set.hasCoeToSort.{u1} M) s) R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} M) Type.{u1} (Set.hasCoeToSort.{u1} M) s) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u2, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} M) Type.{u1} (Set.hasCoeToSort.{u1} M) s) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.semilinearMapClass.{u2, u2, max u1 u2, u1} R R (Finsupp.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} M) Type.{u1} (Set.hasCoeToSort.{u1} M) s) R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} M) Type.{u1} (Set.hasCoeToSort.{u1} M) s) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u2, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} M) Type.{u1} (Set.hasCoeToSort.{u1} M) s) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R _inst_1) (Finsupp.total.{u1, u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} M) Type.{u1} (Set.hasCoeToSort.{u1} M) s) M R _inst_1 _inst_3 _inst_4 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} M) Type.{u1} (Set.hasCoeToSort.{u1} M) s) M (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} M) Type.{u1} (Set.hasCoeToSort.{u1} M) s) M (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} M) Type.{u1} (Set.hasCoeToSort.{u1} M) s) M (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} M) Type.{u1} (Set.hasCoeToSort.{u1} M) s) M (coeSubtype.{succ u1} M (fun (x : M) => Membership.Mem.{u1, u1} M (Set.{u1} M) (Set.hasMem.{u1} M) x s))))))))
but is expected to have type
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Case conversion may be inaccurate. Consider using '#align finsupp.span_eq_range_total Finsupp.span_eq_range_totalₓ'. -/
/-- A version of `finsupp.range_total` which is useful for going in the other direction -/
theorem span_eq_range_total (s : Set M) : span R s = (Finsupp.total s M R coe).range := by
@@ -1118,7 +1118,7 @@ theorem span_eq_range_total (s : Set M) : span R s = (Finsupp.total s M R coe).r
lean 3 declaration is
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but is expected to have type
- forall {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u2} M) (x : M), Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 s)) (Exists.{max (succ u2) (succ u1)} (Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (l : Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} (Set.Elem.{u2} M s) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u1, u1} (Set.Elem.{u2} M s) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u2} R R (Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} (Set.Elem.{u2} M s) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u1, u1} (Set.Elem.{u2} M s) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} (Set.Elem.{u2} M s) M R _inst_1 _inst_3 _inst_4 (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s))) l) x))
+ forall {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u2} M) (x : M), Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 s)) (Exists.{max (succ u2) (succ u1)} (Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (l : Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} (Set.Elem.{u2} M s) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u1, u1} (Set.Elem.{u2} M s) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u2} R R (Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} (Set.Elem.{u2} M s) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u1, u1} (Set.Elem.{u2} M s) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} (Set.Elem.{u2} M s) M R _inst_1 _inst_3 _inst_4 (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s))) l) x))
Case conversion may be inaccurate. Consider using '#align finsupp.mem_span_iff_total Finsupp.mem_span_iff_totalₓ'. -/
theorem mem_span_iff_total (s : Set M) (x : M) :
x ∈ span R s ↔ ∃ l : s →₀ R, Finsupp.total s M R coe l = x :=
@@ -1144,7 +1144,7 @@ variable (R)
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {v : α -> M} (s : Set.{u1} α), Eq.{succ u2} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s)) (Submodule.map.{u3, u3, max u1 u3, u2, max (max u1 u3) u2} R R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomSurjective.ids.{u3} R _inst_1) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.semilinearMapClass.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v) (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {v : α -> M} (s : Set.{u3} α), Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)) (Submodule.map.{u1, u1, max u1 u3, u2, max (max u3 u2) u1} R R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 v) (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s))
+ forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {v : α -> M} (s : Set.{u3} α), Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)) (Submodule.map.{u1, u1, max u1 u3, u2, max (max u3 u2) u1} R R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (LinearMap.semilinearMapClass.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 v) (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s))
Case conversion may be inaccurate. Consider using '#align finsupp.span_image_eq_map_total Finsupp.span_image_eq_map_totalₓ'. -/
theorem span_image_eq_map_total (s : Set α) :
span R (v '' s) = Submodule.map (Finsupp.total α M R v) (supported R R s) :=
@@ -1170,7 +1170,7 @@ theorem span_image_eq_map_total (s : Set α) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {v : α -> M} {s : Set.{u1} α} {x : M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u3, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s))) (Exists.{succ (max u1 u3)} (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (fun (l : Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) => Exists.{0} (Membership.Mem.{max u1 u3, max u1 u3} (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (SetLike.hasMem.{max u1 u3, max u1 u3} (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) (Submodule.setLike.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)))) l (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s)) (fun (H : Membership.Mem.{max u1 u3, max u1 u3} (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (SetLike.hasMem.{max u1 u3, max u1 u3} (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) (Submodule.setLike.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)))) l (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s)) => Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ 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(NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v) l) x)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {v : α -> M} {s : Set.{u3} α} {x : M}, Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (Exists.{succ (max u3 u1)} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (fun (l : Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) => And (Membership.mem.{max u3 u1, max u1 u3} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{max u3 u1, max u3 u1} (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.setLike.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) l (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u1), succ u2} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (a : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) a) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 v) l) x)))
+ forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {v : α -> M} {s : Set.{u3} α} {x : M}, Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (Exists.{succ (max u3 u1)} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (fun (l : Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) => And (Membership.mem.{max u3 u1, max u1 u3} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{max u3 u1, max u3 u1} (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.setLike.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) l (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u1), succ u2} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (a : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) a) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 v) l) x)))
Case conversion may be inaccurate. Consider using '#align finsupp.mem_span_image_iff_total Finsupp.mem_span_image_iff_totalₓ'. -/
theorem mem_span_image_iff_total {s : Set α} {x : M} :
x ∈ span R (v '' s) ↔ ∃ l ∈ supported R R s, Finsupp.total α M R v l = x :=
@@ -1183,7 +1183,7 @@ theorem mem_span_image_iff_total {s : Set α} {x : M} :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (v : (Option.{u1} α) -> M) (f : Finsupp.{u1, u3} (Option.{u1} α) R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} (Option.{u1} α) R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} (Option.{u1} α) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} (Option.{u1} α) M R _inst_1 _inst_3 _inst_4 v) f) (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (Finsupp.{u1, u3} (Option.{u1} α) R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (fun (_x : Finsupp.{u1, u3} (Option.{u1} α) R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) => (Option.{u1} α) -> R) (Finsupp.coeFun.{u1, u3} (Option.{u1} α) R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) f (Option.none.{u1} α)) 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(Semiring.toNonAssocSemiring.{u3} R _inst_1)))) f)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (v : (Option.{u3} α) -> M) (f : Finsupp.{u3, u2} (Option.{u3} α) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} (Option.{u3} α) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) f) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} (Option.{u3} α) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} (Option.{u3} α) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} (Option.{u3} α) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} (Option.{u3} α) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} (Option.{u3} α) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} (Option.{u3} α) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} (Option.{u3} α) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} (Option.{u3} α) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} (Option.{u3} α) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} (Option.{u3} α) M R _inst_1 _inst_3 _inst_4 v) f) (HAdd.hAdd.{u1, u1, u1} M ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) (Finsupp.some.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) f)) M (instHAdd.{u1} M (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (HSMul.hSMul.{u2, u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Option.{u3} α) => R) (Option.none.{u3} α)) M M (instHSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Option.{u3} α) => R) (Option.none.{u3} α)) M (SMulZeroClass.toSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Option.{u3} α) => R) (Option.none.{u3} α)) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Option.{u3} α) => R) (Option.none.{u3} α)) M (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Option.{u3} α) => R) (Option.none.{u3} α)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Option.{u3} α) => R) (Option.none.{u3} α)) _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Option.{u3} α) => R) (Option.none.{u3} α)) M (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Option.{u3} α) => R) (Option.none.{u3} α)) _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Option.{u3} α) => R) (Option.none.{u3} α)) M _inst_1 _inst_3 _inst_4))))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} (Option.{u3} α) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Option.{u3} α) (fun (_x : Option.{u3} α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Option.{u3} α) => R) _x) (Finsupp.funLike.{u3, u2} (Option.{u3} α) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) f (Option.none.{u3} α)) (v (Option.none.{u3} α))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 (Function.comp.{succ u3, succ u3, succ u1} α (Option.{u3} α) M v (Option.some.{u3} α))) (Finsupp.some.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) f)))
+ forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (v : (Option.{u3} α) -> M) (f : Finsupp.{u3, u2} (Option.{u3} α) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} (Option.{u3} α) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) f) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} (Option.{u3} α) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} (Option.{u3} α) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} (Option.{u3} α) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} (Option.{u3} α) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} (Option.{u3} α) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} (Option.{u3} α) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} (Option.{u3} α) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} (Option.{u3} α) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} (Option.{u3} α) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} (Option.{u3} α) M R _inst_1 _inst_3 _inst_4 v) f) (HAdd.hAdd.{u1, u1, u1} M ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) (Finsupp.some.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) f)) M (instHAdd.{u1} M (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (HSMul.hSMul.{u2, u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Option.{u3} α) => R) (Option.none.{u3} α)) M M (instHSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Option.{u3} α) => R) (Option.none.{u3} α)) M (SMulZeroClass.toSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Option.{u3} α) => R) (Option.none.{u3} α)) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Option.{u3} α) => R) (Option.none.{u3} α)) M (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Option.{u3} α) => R) (Option.none.{u3} α)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Option.{u3} α) => R) (Option.none.{u3} α)) _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Option.{u3} α) => R) (Option.none.{u3} α)) M (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Option.{u3} α) => R) (Option.none.{u3} α)) _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Option.{u3} α) => R) (Option.none.{u3} α)) M _inst_1 _inst_3 _inst_4))))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} (Option.{u3} α) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Option.{u3} α) (fun (_x : Option.{u3} α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Option.{u3} α) => R) _x) (Finsupp.funLike.{u3, u2} (Option.{u3} α) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) f (Option.none.{u3} α)) (v (Option.none.{u3} α))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R 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u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 (Function.comp.{succ u3, succ u3, succ u1} α (Option.{u3} α) M v (Option.some.{u3} α))) (Finsupp.some.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) f)))
Case conversion may be inaccurate. Consider using '#align finsupp.total_option Finsupp.total_optionₓ'. -/
theorem total_option (v : Option α → M) (f : Option α →₀ R) :
Finsupp.total (Option α) M R v f =
@@ -1195,7 +1195,7 @@ theorem total_option (v : Option α → M) (f : Option α →₀ R) :
lean 3 declaration is
forall {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {α : Type.{u3}} {β : Type.{u4}} (A : α -> M) (B : β -> (Finsupp.{u3, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (f : Finsupp.{u4, u2} β R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))), Eq.{succ u1} M (coeFn.{max (succ (max u3 u2)) (succ u1), max (succ (max u3 u2)) (succ u1)} (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R 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but is expected to have type
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Case conversion may be inaccurate. Consider using '#align finsupp.total_total Finsupp.total_totalₓ'. -/
theorem total_total {α β : Type _} (A : α → M) (B : β → α →₀ R) (f : β →₀ R) :
Finsupp.total α M R A (Finsupp.total β (α →₀ R) R B f) =
@@ -1246,7 +1246,7 @@ variable {α} {M} {v}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {v : α -> M} (s : Set.{u1} α), Eq.{succ u2} (Submodule.{u3, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u3, u2} R M _inst_1 _inst_3 _inst_4)) (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s))) _inst_1 (Submodule.addCommMonoid.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s))) (Submodule.module.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s)))) (LinearMap.range.{u3, u3, max u1 u3, u2, max (max u1 u3) u2} R R (coeSort.{succ (max u1 u3), succ (succ (max u1 u3))} (Submodule.{u3, max u1 u3} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) Type.{max u1 u3} (SetLike.hasCoeToSort.{max u1 u3, max u1 u3} (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) (Submodule.setLike.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)))) (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s)) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u3, u2} R M _inst_1 _inst_3 _inst_4)) (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s))) (Submodule.addCommMonoid.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s)) (Submodule.addCommMonoid.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s))) (Submodule.module.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s)) (Submodule.module.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R _inst_1) (Finsupp.totalOn.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v s)) (Top.top.{u2} (Submodule.{u3, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u3, u2} R M _inst_1 _inst_3 _inst_4)) 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but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {v : α -> M} (s : Set.{u3} α), Eq.{succ u2} (Submodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (Submodule.module.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))) (LinearMap.range.{u1, u1, max u3 u1, u2, max (max u3 u2) u1} R R (Subtype.{succ (max u3 u1)} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (fun (x : Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) => Membership.mem.{max u3 u1, max u3 u1} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.setLike.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (Submodule.module.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Submodule.module.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.totalOn.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 v s)) (Top.top.{u2} (Submodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (Submodule.module.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))) (Submodule.instTopSubmodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (Submodule.module.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))))
+ forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {v : α -> M} (s : Set.{u3} α), Eq.{succ u2} (Submodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (Submodule.module.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))) (LinearMap.range.{u1, u1, max u3 u1, u2, max (max u3 u2) u1} R R (Subtype.{succ (max u3 u1)} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (fun (x : Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) => Membership.mem.{max u3 u1, max u3 u1} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{max u3 u1, max u3 u1} (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.setLike.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) x (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))) _inst_1 _inst_1 (Submodule.addCommMonoid.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (Submodule.module.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Submodule.module.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Subtype.{succ (max u3 u1)} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (fun (x : Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) => Membership.mem.{max u3 u1, max u3 u1} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{max u3 u1, max u3 u1} (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.setLike.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) x (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))) (Submodule.addCommMonoid.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (Submodule.module.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Submodule.module.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 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Case conversion may be inaccurate. Consider using '#align finsupp.total_on_range Finsupp.totalOn_rangeₓ'. -/
theorem totalOn_range (s : Set α) : (Finsupp.totalOn α M R v s).range = ⊤ :=
by
@@ -1273,7 +1273,7 @@ theorem total_comp (f : α' → α) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {α' : Type.{u4}} {v : α -> M} (f : α -> α') (l : Finsupp.{u4, u3} α' R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (hf : Set.InjOn.{u1, u4} α α' f (Set.preimage.{u1, u4} α α' f ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} α') (Set.{u4} α') (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} α') (Set.{u4} α') (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} α') (Set.{u4} α') (Finset.Set.hasCoeT.{u4} α'))) (Finsupp.support.{u4, u3} α' R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) l)))), Eq.{succ u2} M 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u4) (succ u3)} (Finsupp.{u4, u3} α' R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (fun (_x : Finsupp.{u4, u3} α' R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) => α' -> R) (Finsupp.coeFun.{u4, u3} α' R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) l (f i)) (v i)))
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u1}} (R : Type.{u3}) {_inst_1 : Type.{u4}} [_inst_3 : Semiring.{u3} R] [_inst_4 : AddCommMonoid.{u1} M] [α' : Module.{u3, u1} R M _inst_3 _inst_4] {v : α -> M} (f : α -> _inst_1) (l : Finsupp.{u4, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) (hf : Set.InjOn.{u2, u4} α _inst_1 f (Set.preimage.{u2, u4} α _inst_1 f (Finset.toSet.{u4} _inst_1 (Finsupp.support.{u4, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3)) l)))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) => M) (Finsupp.comapDomain.{u2, u4, u3} α _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3)) f l hf)) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_3 _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3)) (Finsupp.{u2, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) M (Finsupp.addCommMonoid.{u2, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3)))) _inst_4 (Finsupp.module.{u2, u3, u3} α R R _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3))) (Semiring.toModule.{u3} R _inst_3)) α') (Finsupp.{u2, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) (fun (_x : Finsupp.{u2, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) => M) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u1} R R (Finsupp.{u2, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) M _inst_3 _inst_3 (Finsupp.addCommMonoid.{u2, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3)))) _inst_4 (Finsupp.module.{u2, u3, u3} α R R _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3))) (Semiring.toModule.{u3} R _inst_3)) α' (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3))) (Finsupp.total.{u2, u1, u3} α M R _inst_3 _inst_4 α' v) (Finsupp.comapDomain.{u2, u4, u3} α _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3)) f l hf)) (Finset.sum.{u1, u2} M α _inst_4 (Finset.preimage.{u2, u4} α _inst_1 (Finsupp.support.{u4, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3)) l) f hf) (fun (i : α) => HSMul.hSMul.{u3, u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) M M (instHSMul.{u3, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) M (SMulZeroClass.toSMul.{u3, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u3, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) M (MonoidWithZero.toZero.{u3} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) _inst_3)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u3, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) M (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) _inst_3) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (Module.toMulActionWithZero.{u3, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) M _inst_3 _inst_4 α'))))) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Finsupp.{u4, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) _inst_1 (fun (_x : _inst_1) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) _x) (Finsupp.funLike.{u4, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) l (f i)) (v i)))
+ forall {α : Type.{u2}} {M : Type.{u1}} (R : Type.{u3}) {_inst_1 : Type.{u4}} [_inst_3 : Semiring.{u3} R] [_inst_4 : AddCommMonoid.{u1} M] [α' : Module.{u3, u1} R M _inst_3 _inst_4] {v : α -> M} (f : α -> _inst_1) (l : Finsupp.{u4, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) (hf : Set.InjOn.{u2, u4} α _inst_1 f (Set.preimage.{u2, u4} α _inst_1 f (Finset.toSet.{u4} _inst_1 (Finsupp.support.{u4, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3)) l)))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u2, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) => M) (Finsupp.comapDomain.{u2, u4, u3} α _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3)) f l hf)) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_3 _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3)) (Finsupp.{u2, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) M (Finsupp.addCommMonoid.{u2, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3)))) _inst_4 (Finsupp.module.{u2, u3, u3} α R R _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3))) (Semiring.toModule.{u3} R _inst_3)) α') (Finsupp.{u2, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) (fun (_x : Finsupp.{u2, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u2, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) => M) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u1} R R (Finsupp.{u2, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) M _inst_3 _inst_3 (Finsupp.addCommMonoid.{u2, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3)))) _inst_4 (Finsupp.module.{u2, u3, u3} α R R _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3))) (Semiring.toModule.{u3} R _inst_3)) α' (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3))) (Finsupp.total.{u2, u1, u3} α M R _inst_3 _inst_4 α' v) (Finsupp.comapDomain.{u2, u4, u3} α _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3)) f l hf)) (Finset.sum.{u1, u2} M α _inst_4 (Finset.preimage.{u2, u4} α _inst_1 (Finsupp.support.{u4, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3)) l) f hf) (fun (i : α) => HSMul.hSMul.{u3, u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) M M (instHSMul.{u3, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) M (SMulZeroClass.toSMul.{u3, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u3, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) M (MonoidWithZero.toZero.{u3} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) _inst_3)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u3, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) M (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) _inst_3) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (Module.toMulActionWithZero.{u3, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) M _inst_3 _inst_4 α'))))) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Finsupp.{u4, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) _inst_1 (fun (_x : _inst_1) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) _x) (Finsupp.funLike.{u4, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) l (f i)) (v i)))
Case conversion may be inaccurate. Consider using '#align finsupp.total_comap_domain Finsupp.total_comapDomainₓ'. -/
theorem total_comapDomain (f : α → α') (l : α' →₀ R) (hf : Set.InjOn f (f ⁻¹' ↑l.support)) :
Finsupp.total α M R v (Finsupp.comapDomain f l hf) =
@@ -1285,7 +1285,7 @@ theorem total_comapDomain (f : α → α') (l : α' →₀ R) (hf : Set.InjOn f
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {s : Finset.{u1} α} {f : α -> R} (g : α -> M) (hf : forall (a : α), (Ne.{succ u3} R (f a) (OfNat.ofNat.{u3} R 0 (OfNat.mk.{u3} R 0 (Zero.zero.{u3} R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))))) -> (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s)), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 g) (Finsupp.onFinset.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) s f hf)) (Finset.sum.{u2, u1} M α _inst_3 s (fun (x : α) => SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) (f x) (g x)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {s : Finset.{u3} α} {f : α -> R} (g : α -> M) (hf : forall (a : α), (Ne.{succ u2} R (f a) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))))) -> (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) (Finsupp.onFinset.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) s f hf)) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 g) (Finsupp.onFinset.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) s f hf)) (Finset.sum.{u1, u3} M α _inst_3 s (fun (x : α) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4))))) (f x) (g x)))
+ forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {s : Finset.{u3} α} {f : α -> R} (g : α -> M) (hf : forall (a : α), (Ne.{succ u2} R (f a) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))))) -> (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) (Finsupp.onFinset.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) s f hf)) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 g) (Finsupp.onFinset.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) s f hf)) (Finset.sum.{u1, u3} M α _inst_3 s (fun (x : α) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4))))) (f x) (g x)))
Case conversion may be inaccurate. Consider using '#align finsupp.total_on_finset Finsupp.total_onFinsetₓ'. -/
theorem total_onFinset {s : Finset α} {f : α → R} (g : α → M) (hf : ∀ a, f a ≠ 0 → a ∈ s) :
Finsupp.total α M R g (Finsupp.onFinset s f hf) = Finset.sum s fun x : α => f x • g x :=
@@ -1792,7 +1792,7 @@ variable {S}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] {S : Type.{u4}} [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (f : α -> R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R 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but is expected to have type
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(MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (f : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) f) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R 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(α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) f) (Finset.sum.{u4, u3} M α _inst_3 (Finset.univ.{u3} α _inst_1) (fun (i : α) => HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) (f i) (v i)))
+ forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (f : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : α -> R) => M) f) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) v) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearMap.{u1, u1, max u3 u4, max u4 u3 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u3, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) f) (Finset.sum.{u4, u3} M α _inst_3 (Finset.univ.{u3} α _inst_1) (fun (i : α) => HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) (f i) (v i)))
Case conversion may be inaccurate. Consider using '#align fintype.total_apply Fintype.total_applyₓ'. -/
theorem Fintype.total_apply (f) : Fintype.total R S v f = ∑ i, f i • v i :=
rfl
@@ -1802,7 +1802,7 @@ theorem Fintype.total_apply (f) : Fintype.total R S v f = ∑ i, f i • v i :=
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] {S : Type.{u4}} [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (i : α) (r : R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R 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(Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) (Pi.single.{u1, u3} α (fun (ᾰ : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u1} α a b)) (fun (i : α) => MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) i r)) (SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) r (v i))
but is expected to have type
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(MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (i : α) (r : R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) (Pi.single.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} 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_inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) (Pi.single.{u3, u2} α (fun (ᾰ : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) r (v i))
+ forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (i : α) (r : R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : α -> R) => M) (Pi.single.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) v) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearMap.{u1, u1, max u3 u4, max u4 u3 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) (Pi.single.{u3, u2} α (fun (ᾰ : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) r (v i))
Case conversion may be inaccurate. Consider using '#align fintype.total_apply_single Fintype.total_apply_singleₓ'. -/
@[simp]
theorem Fintype.total_apply_single (i : α) (r : R) :
@@ -1818,7 +1818,7 @@ variable (S)
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] (S : Type.{u4}) [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (x : α -> R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R 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u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Finsupp.total.{u1, u2, u3} α M R _inst_2 _inst_3 _inst_4 v) (coeFn.{succ (max u1 u3), succ (max u1 u3)} (LinearEquiv.{u3, u3, max u1 u3, max u1 u3} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHomInvPair.ids.{u3} R _inst_2) (RingHomInvPair.ids.{u3} R _inst_2) (α -> R) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R 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(Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) x)
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (x : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) => M) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (α -> R) (fun (a : α -> R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> R) => Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) a) (SMulHomClass.toFunLike.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R 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(Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (α -> R) (AddMonoid.toZero.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (α -> R) (AddMonoid.toAddZeroClass.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (α -> R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u3 u2, max u3 u2, max u3 u2} R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u3 u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2)))))) (LinearEquiv.symm.{u2, u2, max u3 u2, max u3 u2} R R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (α -> R) _inst_2 _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (Finsupp.linearEquivFunOnFinite.{u2, u2, u3} R R α (Finite.of_fintype.{u3} α _inst_1) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R 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(Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) x)
+ forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (x : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) => M) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (α -> R) (fun (a : α -> R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> R) => Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) a) (SMulHomClass.toFunLike.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (α -> R) (AddMonoid.toZero.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (α -> R) (AddMonoid.toAddZeroClass.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (α -> R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u3 u2, max u3 u2, max u3 u2} R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u3 u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R 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Case conversion may be inaccurate. Consider using '#align finsupp.total_eq_fintype_total_apply Finsupp.total_eq_fintype_total_applyₓ'. -/
theorem Finsupp.total_eq_fintype_total_apply (x : α → R) :
Finsupp.total α M R v ((Finsupp.linearEquivFunOnFinite R R α).symm x) = Fintype.total R S v x :=
@@ -1834,7 +1834,7 @@ theorem Finsupp.total_eq_fintype_total_apply (x : α → R) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] (S : Type.{u4}) [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (LinearMap.comp.{u3, u3, u3, max u1 u3, max u1 u3, u2} R R R (α -> R) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))) M _inst_2 _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHomCompTriple.right_ids.{u3, u3} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Finsupp.total.{u1, u2, u3} α M R _inst_2 _inst_3 _inst_4 v) (LinearEquiv.toLinearMap.{u3, u3, max u1 u3, max u1 u3} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHomInvPair.ids.{u3} R _inst_2) (RingHomInvPair.ids.{u3} R _inst_2) (α -> R) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))))) (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) (LinearEquiv.symm.{u3, u3, max u1 u3, max u1 u3} R R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))))) (α -> R) _inst_2 _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHomInvPair.ids.{u3} R _inst_2) (RingHomInvPair.ids.{u3} R _inst_2) (Finsupp.linearEquivFunOnFinite.{u3, u3, u1} R R α (Finite.of_fintype.{u1} α _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) _inst_2 (Semiring.toModule.{u3} R _inst_2))))) (coeFn.{max (succ (max u1 u2)) (succ (max (max u1 u3) u2)), max (succ (max u1 u2)) (succ (max (max u1 u3) u2))} (LinearMap.{u4, u4, max u1 u2, max (max u1 u3) u2} S S _inst_5 _inst_5 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4)) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, max (max u1 u3) u2} S S (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)
but is expected to have type
- forall {α : Type.{u4}} {M : Type.{u3}} (R : Type.{u2}) [_inst_1 : Fintype.{u4} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u3} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u3} R S M (SMulZeroClass.toSMul.{u2, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u2, u3} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u3} S M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u1, u3} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (LinearMap.comp.{u2, u2, u2, max u4 u2, max u4 u2, u3} R R R (α -> R) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) M _inst_2 _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomCompTriple.ids.{u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Finsupp.total.{u4, u3, u2} α M R _inst_2 _inst_3 _inst_4 v) (LinearEquiv.toLinearMap.{u2, u2, max u4 u2, max u4 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u4, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (LinearEquiv.symm.{u2, u2, max u4 u2, max u4 u2} R R (Finsupp.{u4, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (α -> R) _inst_2 _inst_2 (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (Finsupp.linearEquivFunOnFinite.{u2, u2, u4} R R α (Finite.of_fintype.{u4} α _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) _inst_2 (Semiring.toModule.{u2} R _inst_2))))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), max (max (succ u2) (succ u3)) (succ u4)} (LinearMap.{u1, u1, max u4 u3, max u3 u4 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u4, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u4 u2, u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u4, u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u4 u2, u3} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u4, max (max u2 u3) u4} S S (α -> M) (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u4, u3} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u4 u2, u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u4, u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u4 u2, u3} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u4, u3, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)
+ forall {α : Type.{u4}} {M : Type.{u3}} (R : Type.{u2}) [_inst_1 : Fintype.{u4} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u3} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u3} R S M (SMulZeroClass.toSMul.{u2, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u2, u3} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u3} S M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u1, u3} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (LinearMap.comp.{u2, u2, u2, max u4 u2, max u4 u2, u3} R R R (α -> R) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) M _inst_2 _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomCompTriple.ids.{u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Finsupp.total.{u4, u3, u2} α M R _inst_2 _inst_3 _inst_4 v) (LinearEquiv.toLinearMap.{u2, u2, max u4 u2, max u4 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u4, u2} α R (AddMonoid.toZero.{u2} R 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_inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u4, u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u4 u2, u3} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u4, u3, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)
Case conversion may be inaccurate. Consider using '#align finsupp.total_eq_fintype_total Finsupp.total_eq_fintype_totalₓ'. -/
theorem Finsupp.total_eq_fintype_total :
(Finsupp.total α M R v).comp (Finsupp.linearEquivFunOnFinite R R α).symm.toLinearMap =
@@ -1848,7 +1848,7 @@ variable {S}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] {S : Type.{u4}} [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{succ u2} (Submodule.{u3, u2} R M _inst_2 _inst_3 _inst_4) (LinearMap.range.{u3, u3, max u1 u3, u2, max (max u1 u3) u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (LinearMap.semilinearMapClass.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (RingHomSurjective.ids.{u3} R _inst_2) (coeFn.{max (succ (max u1 u2)) (succ (max (max u1 u3) u2)), max (succ (max u1 u2)) (succ (max (max u1 u3) u2))} (LinearMap.{u4, u4, max u1 u2, max (max u1 u3) u2} S S _inst_5 _inst_5 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) (fun (_x : LinearMap.{u4, u4, max u1 u2, max (max u1 u3) u2} S S _inst_5 _inst_5 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) => (α -> M) -> (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4)) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, max (max u1 u3) u2} S S (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)) (Submodule.span.{u3, u2} R M _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u1} M α v))
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u4}} (R : Type.{u3}) [_inst_1 : Fintype.{u2} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u3, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u1, u4} R S M (SMulZeroClass.toSMul.{u3, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u4} R M (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u4} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u3, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{succ u4} (Submodule.{u3, u4} R M _inst_2 _inst_3 _inst_4) (LinearMap.range.{u3, u3, max u2 u3, u4, max (max u2 u4) u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) v) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (RingHomSurjective.ids.{u3} R _inst_2) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearMap.{u1, u1, max u2 u4, max u4 u2 u3} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u2, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun 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(Pi.module.{u2, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u2 u3, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u2, u4, u3, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)) (Submodule.span.{u3, u4} R M _inst_2 _inst_3 _inst_4 (Set.range.{u4, succ u2} M α v))
+ forall {α : Type.{u2}} {M : Type.{u4}} (R : Type.{u3}) [_inst_1 : Fintype.{u2} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u3, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u1, u4} R S M (SMulZeroClass.toSMul.{u3, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u4} R M (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u4} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u3, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{succ u4} (Submodule.{u3, u4} R M _inst_2 _inst_3 _inst_4) (LinearMap.range.{u3, u3, max u2 u3, u4, max (max u2 u4) u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : α -> M) => LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) v) (LinearMap.semilinearMapClass.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (RingHomSurjective.ids.{u3} R _inst_2) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearMap.{u1, u1, max u2 u4, max u4 u2 u3} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u2, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : α -> M) => LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u2, max (max u3 u4) u2} S S (α -> M) (LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u2, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.module.{u2, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u2 u3, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u2, u4, u3, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)) (Submodule.span.{u3, u4} R M _inst_2 _inst_3 _inst_4 (Set.range.{u4, succ u2} M α v))
Case conversion may be inaccurate. Consider using '#align fintype.range_total Fintype.range_totalₓ'. -/
@[simp]
theorem Fintype.range_total : (Fintype.total R S v).range = Submodule.span R (Set.range v) := by
@@ -1920,7 +1920,7 @@ irreducible_def Span.repr (w : Set M) (x : span R w) : w →₀ R :=
lean 3 declaration is
forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {w : Set.{u2} M} (x : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w)), Eq.{succ u2} M (coeFn.{max (succ (max u2 u1)) (succ u2), max (succ (max u2 u1)) (succ u2)} (LinearMap.{u1, u1, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) w) R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (Finsupp.addCommMonoid.{u2, u1} 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(Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w)) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w)) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w)) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w)) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w)))))) x)
but is expected to have type
- forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {w : Set.{u2} M} (x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) (Span.repr.{u1, u2} R M _inst_1 _inst_2 _inst_3 w x)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} (Set.Elem.{u2} M w) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} (Set.Elem.{u2} M w) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) (Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u2} R R (Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} (Set.Elem.{u2} M w) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} (Set.Elem.{u2} M w) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} (Set.Elem.{u2} M w) M R _inst_1 _inst_2 _inst_3 (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x w))) (Span.repr.{u1, u2} R M _inst_1 _inst_2 _inst_3 w x)) (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w))) x)
+ forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {w : Set.{u2} M} (x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) (Span.repr.{u1, u2} R M _inst_1 _inst_2 _inst_3 w x)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} (Set.Elem.{u2} M w) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} (Set.Elem.{u2} M w) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) (Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u2} R R (Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} (Set.Elem.{u2} M w) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} (Set.Elem.{u2} M w) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} (Set.Elem.{u2} M w) M R _inst_1 _inst_2 _inst_3 (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x w))) (Span.repr.{u1, u2} R M _inst_1 _inst_2 _inst_3 w x)) (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w))) x)
Case conversion may be inaccurate. Consider using '#align span.finsupp_total_repr Span.finsupp_total_reprₓ'. -/
@[simp]
theorem Span.finsupp_total_repr {w : Set M} (x : span R w) :
@@ -1947,7 +1947,7 @@ protected theorem Submodule.finsupp_sum_mem {ι β : Type _} [Zero β] (S : Subm
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_4] (f : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M N _inst_2 _inst_4 _inst_3 _inst_5) {ι : Type.{u4}} {g : ι -> M} (l : Finsupp.{u4, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))), Eq.{succ u3} N (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M N _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M N _inst_2 _inst_4 _inst_3 _inst_5) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M N _inst_1 _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u4, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (Finsupp.addCommMonoid.{u4, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u4, u1, u1} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u4, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (Finsupp.addCommMonoid.{u4, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u4, u1, u1} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) => (Finsupp.{u4, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} R R (Finsupp.{u4, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u4, u1, u1} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u4, u2, u1} ι M R _inst_1 _inst_2 _inst_3 g) l)) (coeFn.{max (succ (max u4 u1)) (succ u3), max (succ (max u4 u1)) (succ u3)} (LinearMap.{u1, u1, max u4 u1, 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) N (Finsupp.addCommMonoid.{u4, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_4 (Finsupp.module.{u4, u1, u1} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_5) => (Finsupp.{u4, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) -> N) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u3} R R (Finsupp.{u4, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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(x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u4 u1, u3} R R (Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u4, u4} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Finsupp.total.{u1, u3, u4} ι M R _inst_1 _inst_2 _inst_3 g) l)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u1), max (succ u4) (succ u1), succ u2} (LinearMap.{u4, u4, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) N (Finsupp.addCommMonoid.{u1, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_4 (Finsupp.module.{u1, u4, u4} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_5) (Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) (fun (_x : Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u4 u1, u2} R R (Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_4 (Finsupp.module.{u1, u4, u4} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Finsupp.total.{u1, u2, u4} ι N R _inst_1 _inst_4 _inst_5 (Function.comp.{succ u1, succ u3, succ u2} ι M N (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (LinearMap.{u4, u4, u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_2 _inst_4 _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, u2} R R M N _inst_1 _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) f) g)) l)
Case conversion may be inaccurate. Consider using '#align linear_map.map_finsupp_total LinearMap.map_finsupp_totalₓ'. -/
theorem LinearMap.map_finsupp_total (f : M →ₗ[R] N) {ι : Type _} {g : ι → M} (l : ι →₀ R) :
f (Finsupp.total ι M R g l) = Finsupp.total ι N R (f ∘ g) l := by
@@ -2043,7 +2043,7 @@ open Finsupp Function
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_1 _inst_1 _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3)
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} (f : LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u1) (succ u3)} M (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u3} R R M (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _inst_1 _inst_1 _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} (f : LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u1) (succ u3)} M (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u3} R R M (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _inst_1 _inst_1 _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3)
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_finsupp_surjective LinearMap.splittingOfFinsuppSurjectiveₓ'. -/
-- See also `linear_map.splitting_of_fun_on_fintype_surjective`
/-- A surjective linear map to finitely supported functions has a splitting. -/
@@ -2055,7 +2055,7 @@ def splittingOfFinsuppSurjective (f : M →ₗ[R] α →₀ R) (s : Surjective f
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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but is expected to have type
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (LinearMap.comp.{u3, u3, u3, max u3 u1, u2, max u3 u1} R R R (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} 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+ forall {R : Type.{u3}} {M : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u3, u2} R M _inst_1 _inst_2] {α : Type.{u1}} (f : LinearMap.{u3, u3, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (FunLike.coe.{max 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(MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_1 _inst_1 _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)), Eq.{max (succ u3) (succ u1)} (LinearMap.{u3, u3, max u3 u1, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (LinearMap.comp.{u3, u3, u3, max u3 u1, u2, max u3 u1} R R R (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomCompTriple.ids.{u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f (LinearMap.splittingOfFinsuppSurjective.{u3, u2, u1} R M _inst_1 _inst_2 _inst_3 α f s)) (LinearMap.id.{u3, max u3 u1} R (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)))
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_finsupp_surjective_splits LinearMap.splittingOfFinsuppSurjective_splitsₓ'. -/
theorem splittingOfFinsuppSurjective_splits (f : M →ₗ[R] α →₀ R) (s : Surjective f) :
f.comp (splittingOfFinsuppSurjective f s) = LinearMap.id :=
@@ -2072,7 +2072,7 @@ theorem splittingOfFinsuppSurjective_splits (f : M →ₗ[R] α →₀ R) (s : S
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M 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_inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_1 _inst_1 _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Function.LeftInverse.{max (succ u3) (succ u1), succ u2} (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 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but is expected to have type
- forall {R : Type.{u3}} {M : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u3, u2} R M _inst_1 _inst_2] {α : Type.{u1}} (f : LinearMap.{u3, u3, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (FunLike.coe.{max 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+ forall {R : Type.{u3}} {M : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u3, u2} R M _inst_1 _inst_2] {α : Type.{u1}} (f : LinearMap.{u3, u3, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (FunLike.coe.{max 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.splittingOfFinsuppSurjective.{u3, u2, u1} R M _inst_1 _inst_2 _inst_3 α f s))
Case conversion may be inaccurate. Consider using '#align linear_map.left_inverse_splitting_of_finsupp_surjective LinearMap.leftInverse_splittingOfFinsuppSurjectiveₓ'. -/
theorem leftInverse_splittingOfFinsuppSurjective (f : M →ₗ[R] α →₀ R) (s : Surjective f) :
LeftInverse f (splittingOfFinsuppSurjective f s) := fun g =>
@@ -2083,7 +2083,7 @@ theorem leftInverse_splittingOfFinsuppSurjective (f : M →ₗ[R] α →₀ R) (
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M 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(Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_1 _inst_1 _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Function.Injective.{max (succ u3) (succ u1), succ u2} (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R 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(MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.splittingOfFinsuppSurjective.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 α f s))
but is expected to have type
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+ forall {R : Type.{u3}} {M : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u3, u2} R M _inst_1 _inst_2] {α : Type.{u1}} (f : LinearMap.{u3, u3, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u2, max (succ u3) (succ u1)} (LinearMap.{u3, u3, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, max u3 u1} R R M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_1 _inst_1 _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)), Function.Injective.{max (succ u3) (succ u1), succ u2} (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u1), succ u2} (LinearMap.{u3, u3, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_3) (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (fun (_x : Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u1, u2} R R (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.splittingOfFinsuppSurjective.{u3, u2, u1} R M _inst_1 _inst_2 _inst_3 α f s))
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_finsupp_surjective_injective LinearMap.splittingOfFinsuppSurjective_injectiveₓ'. -/
theorem splittingOfFinsuppSurjective_injective (f : M →ₗ[R] α →₀ R) (s : Surjective f) :
Injective (splittingOfFinsuppSurjective f s) :=
@@ -2094,7 +2094,7 @@ theorem splittingOfFinsuppSurjective_injective (f : M →ₗ[R] α →₀ R) (s
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3)
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u1) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) _inst_3)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u1) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) _inst_3)
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective LinearMap.splittingOfFunOnFintypeSurjectiveₓ'. -/
-- See also `linear_map.splitting_of_finsupp_surjective`
/-- A surjective linear map to functions on a finite type has a splitting. -/
@@ -2108,7 +2108,7 @@ def splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R) (s
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Eq.{succ (max u3 u1)} (LinearMap.{u1, u1, max u3 u1, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (LinearMap.comp.{u1, u1, u1, max u3 u1, u2, max u3 u1} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomCompTriple.right_ids.{u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u1, max u3 u1} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17208 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17208 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17208 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17208 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Eq.{max (succ u2) (succ u3)} (LinearMap.{u2, u2, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17208 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.comp.{u2, u2, u2, max u2 u3, u1, max u2 u3} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17208 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u2, max u2 u3} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17208 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17208 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17208 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17208 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Eq.{max (succ u2) (succ u3)} (LinearMap.{u2, u2, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17208 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.comp.{u2, u2, u2, max u2 u3, u1, max u2 u3} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17208 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u2, max u2 u3} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)))
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective_splits LinearMap.splittingOfFunOnFintypeSurjective_splitsₓ'. -/
theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : f.comp (splittingOfFunOnFintypeSurjective f s) = LinearMap.id :=
@@ -2124,7 +2124,7 @@ theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R]
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Function.LeftInverse.{max (succ u3) (succ u1), succ u2} (α -> R) M (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f) (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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but is expected to have type
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => 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+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17340 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), 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Case conversion may be inaccurate. Consider using '#align linear_map.left_inverse_splitting_of_fun_on_fintype_surjective LinearMap.leftInverse_splittingOfFunOnFintypeSurjectiveₓ'. -/
theorem leftInverse_splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : LeftInverse f (splittingOfFunOnFintypeSurjective f s) := fun g =>
@@ -2135,7 +2135,7 @@ theorem leftInverse_splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Function.Injective.{max (succ u3) (succ u1), succ u2} (α -> R) M (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) (fun (_x : LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) => (α -> R) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, u2} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17399 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17399 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17399 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17399 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Function.Injective.{max (succ u2) (succ u3), succ u1} (α -> R) M (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17399 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17399 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17399 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17399 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Function.Injective.{max (succ u2) (succ u3), succ u1} (α -> R) M (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective_injective LinearMap.splittingOfFunOnFintypeSurjective_injectiveₓ'. -/
theorem splittingOfFunOnFintypeSurjective_injective [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : Injective (splittingOfFunOnFintypeSurjective f s) :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
@@ -212,7 +212,7 @@ theorem ker_lsingle (a : α) : (lsingle a : M →ₗ[R] α →₀ M).ker = ⊥ :
/- warning: finsupp.lsingle_range_le_ker_lapply -> Finsupp.lsingle_range_le_ker_lapply is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α) (t : Set.{u1} α), (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) s t) -> (LE.le.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toLE.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))))) (iSup.{max u1 u2, succ u1} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => iSup.{max u1 u2, 0} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LinearMap.range.{u3, u3, u2, max u1 u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u3, u3, u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R _inst_1) (Finsupp.lsingle.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a)))) (iInf.{max u1 u2, succ u1} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasInf.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) α (fun (a : α) => iInf.{max u1 u2, 0} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasInf.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a t) => LinearMap.ker.{u3, u3, max u1 u2, u2, max u1 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4) (LinearMap.semilinearMapClass.{u3, u3, max u1 u2, u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lapply.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a)))))
+ forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α) (t : Set.{u1} α), (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) s t) -> (LE.le.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toHasLe.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))))) (iSup.{max u1 u2, succ u1} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => iSup.{max u1 u2, 0} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LinearMap.range.{u3, u3, u2, max u1 u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u3, u3, u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R _inst_1) (Finsupp.lsingle.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a)))) (iInf.{max u1 u2, succ u1} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasInf.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) α (fun (a : α) => iInf.{max u1 u2, 0} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasInf.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a t) => LinearMap.ker.{u3, u3, max u1 u2, u2, max u1 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4) (LinearMap.semilinearMapClass.{u3, u3, max u1 u2, u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lapply.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a)))))
but is expected to have type
forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (t : Set.{u3} α), (Disjoint.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} α) (Preorder.toLE.{u3} (Set.{u3} α) (PartialOrder.toPreorder.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) s t) -> (LE.le.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toLE.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))))) (iSup.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => iSup.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) (fun (H : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a)))) (iInf.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) α (fun (a : α) => iInf.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a t) (fun (H : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a t) => LinearMap.ker.{u1, u1, max u3 u2, u2, max u3 u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u3 u2, u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lapply.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a)))))
Case conversion may be inaccurate. Consider using '#align finsupp.lsingle_range_le_ker_lapply Finsupp.lsingle_range_le_ker_lapplyₓ'. -/
@@ -228,7 +228,7 @@ theorem lsingle_range_le_ker_lapply (s t : Set α) (h : Disjoint s t) :
/- warning: finsupp.infi_ker_lapply_le_bot -> Finsupp.iInf_ker_lapply_le_bot is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], LE.le.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toLE.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))))) (iInf.{max u1 u2, succ u1} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasInf.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) α (fun (a : α) => LinearMap.ker.{u3, u3, max u1 u2, u2, max u1 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4) (LinearMap.semilinearMapClass.{u3, u3, max u1 u2, u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lapply.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a))) (Bot.bot.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasBot.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))
+ forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], LE.le.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toHasLe.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))))) (iInf.{max u1 u2, succ u1} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasInf.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) α (fun (a : α) => LinearMap.ker.{u3, u3, max u1 u2, u2, max u1 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4) (LinearMap.semilinearMapClass.{u3, u3, max u1 u2, u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lapply.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a))) (Bot.bot.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasBot.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))
but is expected to have type
forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], LE.le.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toLE.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))))) (iInf.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) α (fun (a : α) => LinearMap.ker.{u1, u1, max u3 u2, u2, max u3 u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u3 u2, u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lapply.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a))) (Bot.bot.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instBotSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))
Case conversion may be inaccurate. Consider using '#align finsupp.infi_ker_lapply_le_bot Finsupp.iInf_ker_lapply_le_botₓ'. -/
@@ -436,7 +436,7 @@ theorem range_restrictDom (s : Set α) : (restrictDom M R s).range = ⊤ :=
/- warning: finsupp.supported_mono -> Finsupp.supported_mono is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s t) -> (LE.le.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toLE.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))))) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 t))
+ forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s t) -> (LE.le.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toHasLe.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))))) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 t))
but is expected to have type
forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {s : Set.{u3} α} {t : Set.{u3} α}, (HasSubset.Subset.{u3} (Set.{u3} α) (Set.instHasSubsetSet.{u3} α) s t) -> (LE.le.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toLE.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))))) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 t))
Case conversion may be inaccurate. Consider using '#align finsupp.supported_mono Finsupp.supported_monoₓ'. -/
@@ -786,7 +786,7 @@ theorem lmapDomain_comp (f : α → α') (g : α' → α'') :
/- warning: finsupp.supported_comap_lmap_domain -> Finsupp.supported_comap_lmapDomain is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {α' : Type.{u4}} (f : α -> α') (s : Set.{u4} α'), LE.le.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toLE.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))))) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (Set.preimage.{u1, u4} α α' f s)) (Submodule.comap.{u3, u3, max u1 u2, max u4 u2, max (max u1 u2) u4 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, max u1 u2, max u4 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u3, u3, max u1 u2, max u4 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lmapDomain.{u1, u2, u3, u4} α M R _inst_1 _inst_3 _inst_4 α' f) (Finsupp.supported.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4 s))
+ forall {α : Type.{u1}} (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {α' : Type.{u4}} (f : α -> α') (s : Set.{u4} α'), LE.le.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toHasLe.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))))) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (Set.preimage.{u1, u4} α α' f s)) (Submodule.comap.{u3, u3, max u1 u2, max u4 u2, max (max u1 u2) u4 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, max u1 u2, max u4 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u3, u3, max u1 u2, max u4 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lmapDomain.{u1, u2, u3, u4} α M R _inst_1 _inst_3 _inst_4 α' f) (Finsupp.supported.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4 s))
but is expected to have type
forall {α : Type.{u3}} (M : Type.{u2}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {α' : Type.{u4}} (f : α -> α') (s : Set.{u4} α'), LE.le.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toLE.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))))) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (Set.preimage.{u3, u4} α α' f s)) (Submodule.comap.{u1, u1, max u3 u2, max u2 u4, max (max u2 u4) u3} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, max u2 u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u1} α' M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u3 u2, max u2 u4} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lmapDomain.{u3, u2, u1, u4} α M R _inst_1 _inst_3 _inst_4 α' f) (Finsupp.supported.{u4, u2, u1} α' M R _inst_1 _inst_3 _inst_4 s))
Case conversion may be inaccurate. Consider using '#align finsupp.supported_comap_lmap_domain Finsupp.supported_comap_lmapDomainₓ'. -/
@@ -1877,7 +1877,7 @@ theorem mem_span_range_iff_exists_fun : x ∈ span R (range v) ↔ ∃ c : α
/- warning: top_le_span_range_iff_forall_exists_fun -> top_le_span_range_iff_forall_exists_fun is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] {v : α -> M}, Iff (LE.le.{u2} (Submodule.{u3, u2} R M _inst_2 _inst_3 _inst_4) (Preorder.toLE.{u2} (Submodule.{u3, u2} R M _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} R M _inst_2 _inst_3 _inst_4) (SetLike.partialOrder.{u2, u2} (Submodule.{u3, u2} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (Top.top.{u2} (Submodule.{u3, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.hasTop.{u3, u2} R M _inst_2 _inst_3 _inst_4)) (Submodule.span.{u3, u2} R M _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u1} M α v))) (forall (x : M), Exists.{max (succ u1) (succ u3)} (α -> R) (fun (c : α -> R) => Eq.{succ u2} M (Finset.sum.{u2, u1} M α _inst_3 (Finset.univ.{u1} α _inst_1) (fun (i : α) => SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (c i) (v i))) x))
+ forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] {v : α -> M}, Iff (LE.le.{u2} (Submodule.{u3, u2} R M _inst_2 _inst_3 _inst_4) (Preorder.toHasLe.{u2} (Submodule.{u3, u2} R M _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} R M _inst_2 _inst_3 _inst_4) (SetLike.partialOrder.{u2, u2} (Submodule.{u3, u2} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (Top.top.{u2} (Submodule.{u3, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.hasTop.{u3, u2} R M _inst_2 _inst_3 _inst_4)) (Submodule.span.{u3, u2} R M _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u1} M α v))) (forall (x : M), Exists.{max (succ u1) (succ u3)} (α -> R) (fun (c : α -> R) => Eq.{succ u2} M (Finset.sum.{u2, u1} M α _inst_3 (Finset.univ.{u1} α _inst_1) (fun (i : α) => SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (c i) (v i))) x))
but is expected to have type
forall {α : Type.{u1}} {M : Type.{u3}} (R : Type.{u2}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_2 _inst_3] {v : α -> M}, Iff (LE.le.{u3} (Submodule.{u2, u3} R M _inst_2 _inst_3 _inst_4) (Preorder.toLE.{u3} (Submodule.{u2, u3} R M _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (Submodule.{u2, u3} R M _inst_2 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R M _inst_2 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R M _inst_2 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u3} R M _inst_2 _inst_3 _inst_4))))) (Top.top.{u3} (Submodule.{u2, u3} R M _inst_2 _inst_3 _inst_4) (Submodule.instTopSubmodule.{u2, u3} R M _inst_2 _inst_3 _inst_4)) (Submodule.span.{u2, u3} R M _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u1} M α v))) (forall (x : M), Exists.{max (succ u1) (succ u2)} (α -> R) (fun (c : α -> R) => Eq.{succ u3} M (Finset.sum.{u3, u1} M α _inst_3 (Finset.univ.{u1} α _inst_1) (fun (i : α) => HSMul.hSMul.{u2, u3, u3} R M M (instHSMul.{u2, u3} R M (SMulZeroClass.toSMul.{u2, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u2, u3} R M _inst_2 _inst_3 _inst_4))))) (c i) (v i))) x))
Case conversion may be inaccurate. Consider using '#align top_le_span_range_iff_forall_exists_fun top_le_span_range_iff_forall_exists_funₓ'. -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
@@ -670,7 +670,7 @@ noncomputable def lift : (X → M) ≃+ ((X →₀ R) →ₗ[R] M) :=
lean 3 declaration is
forall (M : Type.{u1}) (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u3}) (f : LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (x : X), Eq.{succ u1} M (coeFn.{max (succ (max (max u3 u2) u1)) (succ 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(NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))))))
but is expected to have type
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R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => X -> M) _x) (AddHomClass.toFunLike.{max (max u1 u3) u2, max (max u1 u3) u2, max u1 u2} (AddEquiv.{max (max u1 u3) u2, max u1 u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (LinearMap.instAddLinearMap.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.instAdd.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5047 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (AddZeroClass.toAdd.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddMonoid.toAddZeroClass.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (AddZeroClass.toAdd.{max u1 u2} (X -> M) (Pi.addZeroClass.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5047 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (AddMonoidHomClass.toAddHomClass.{max (max u1 u3) u2, max (max u1 u3) u2, max u1 u2} (AddEquiv.{max (max u1 u3) u2, max u1 u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (LinearMap.instAddLinearMap.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.instAdd.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5047 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (AddMonoid.toAddZeroClass.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Pi.addZeroClass.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5047 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddEquivClass.instAddMonoidHomClass.{max (max u1 u3) u2, max (max u1 u3) u2, max u1 u2} (AddEquiv.{max (max u1 u3) u2, max u1 u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (LinearMap.instAddLinearMap.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.instAdd.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5047 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (AddMonoid.toAddZeroClass.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Pi.addZeroClass.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5047 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddEquiv.instAddEquivClassAddEquiv.{max (max u1 u3) u2, max u1 u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (LinearMap.instAddLinearMap.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.instAdd.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5047 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))) (AddEquiv.symm.{max u1 u2, max (max u1 u3) u2} (X -> M) (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 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Case conversion may be inaccurate. Consider using '#align finsupp.lift_symm_apply Finsupp.lift_symm_applyₓ'. -/
@[simp]
theorem lift_symm_apply (f) (x) : ((lift M R X).symm f) x = f (single x 1) :=
@@ -681,7 +681,7 @@ theorem lift_symm_apply (f) (x) : ((lift M R X).symm f) x = f (single x 1) :=
lean 3 declaration is
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(Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (ᾰ : X) => M) (fun (i : X) => AddZeroClass.toHasAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.hasAdd.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.lift.{u1, u2, u3} M R _inst_1 _inst_3 _inst_4 X) f) g) (Finsupp.sum.{u3, u2, u1} X R M (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 g (fun (x : X) (r : R) => SMul.smul.{u2, u1} R M (SMulZeroClass.toHasSmul.{u2, u1} R M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u1} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4)))) r (f x)))
but is expected to have type
- forall (M : Type.{u1}) (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u3}) (f : X -> M) (g : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) g) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : X -> M) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) f) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (max (succ u1) (succ u2)) (succ u3)} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R 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(Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (fun (_x : X -> M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : X -> M) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) _x) (AddHomClass.toFunLike.{max (max u1 u2) u3, max u1 u3, max (max u1 u2) u3} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (AddMonoidHomClass.toAddHomClass.{max (max u1 u2) u3, max u1 u3, max (max u1 u2) u3} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5047 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.addZeroClass.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5047 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddEquivClass.instAddMonoidHomClass.{max (max u1 u2) u3, max u1 u3, max (max u1 u2) u3} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5047 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.addZeroClass.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5047 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddEquiv.instAddEquivClassAddEquiv.{max u1 u3, max (max u1 u2) u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5047 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (Finsupp.lift.{u1, u2, u3} M R _inst_1 _inst_3 _inst_4 X) f) g) (Finsupp.sum.{u3, u2, u1} X R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) _inst_3 g (fun (x : X) (r : R) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4))))) r (f x)))
+ forall (M : Type.{u1}) (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u3}) (f : X -> M) (g : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) g) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : X -> M) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) f) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (FunLike.coe.{max (succ (max u1 u3)) (succ (max (max u1 u2) u3)), succ (max u1 u3), succ (max (max u1 u2) u3)} (AddEquiv.{max u1 u3, max (max u1 u2) u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5047 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (fun (_x : X -> M) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : X -> M) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) _x) (EmbeddingLike.toFunLike.{max (succ (max u1 u3)) (succ (max (max u1 u2) u3)), succ (max u1 u3), succ (max (max u1 u2) u3)} (AddEquiv.{max u1 u3, max (max u1 u2) u3} (X -> M) (LinearMap.{u2, u2, max u2 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (Finsupp.lift.{u1, u2, u3} M R _inst_1 _inst_3 _inst_4 X) f) g) (Finsupp.sum.{u3, u2, u1} X R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) _inst_3 g (fun (x : X) (r : R) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4))))) r (f x)))
Case conversion may be inaccurate. Consider using '#align finsupp.lift_apply Finsupp.lift_applyₓ'. -/
@[simp]
theorem lift_apply (f) (g) : ((lift M R X) f) g = g.Sum fun x r => r • f x :=
@@ -711,7 +711,7 @@ noncomputable def llift : (X → M) ≃ₗ[S] (X →₀ R) →ₗ[R] M :=
lean 3 declaration is
forall (M : Type.{u1}) (R : Type.{u2}) (S : Type.{u3}) [_inst_1 : Semiring.{u2} R] [_inst_2 : Semiring.{u3} S] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u4}) [_inst_9 : Module.{u3, u1} S M _inst_2 _inst_3] [_inst_10 : SMulCommClass.{u2, u3, u1} R S M (SMulZeroClass.toHasSmul.{u2, u1} R M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u1} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u3, u1} S M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u1} S M (MulZeroClass.toHasZero.{u3} S (MulZeroOneClass.toMulZeroClass.{u3} S (MonoidWithZero.toMulZeroOneClass.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)))) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u1} S M (Semiring.toMonoidWithZero.{u3} S _inst_2) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Module.toMulActionWithZero.{u3, u1} S M _inst_2 _inst_3 _inst_9))))] (f : X -> M) (x : Finsupp.{u4, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))), Eq.{succ u1} M 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u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) => (X -> M) -> (LinearMap.{u2, u2, max u4 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u4, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u4, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4)) (AddEquiv.hasCoeToFun.{max u4 u1, max (max u4 u2) u1} (X -> M) (LinearMap.{u2, u2, max u4 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u4, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u4, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u4, u1} X (fun (ᾰ : X) => M) (fun (i : X) => AddZeroClass.toHasAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.hasAdd.{u2, u2, max u4 u2, u1} R R (Finsupp.{u4, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.lift.{u1, u2, u4} M R _inst_1 _inst_3 _inst_4 X) f) x)
but is expected to have type
- forall (M : Type.{u2}) (R : Type.{u3}) (S : Type.{u1}) [_inst_1 : Semiring.{u3} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (X : Type.{u4}) [_inst_9 : Module.{u1, u2} S M _inst_2 _inst_3] [_inst_10 : SMulCommClass.{u3, u1, u2} R S M (SMulZeroClass.toSMul.{u3, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u2} R M (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} S M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} S M (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u1, u2} S M _inst_2 _inst_3 _inst_9))))] (f : X -> M) (x : Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) => M) x) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : X -> M) => LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) f) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (fun (_x : Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u2) (succ u4), max (max (succ u2) (succ u3)) (succ u4)} (LinearEquiv.{u1, u1, max u2 u4, max u2 u3 u4} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_2 _inst_9 _inst_10)) (X -> M) (fun (_x : X -> M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : X -> M) => LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) _x) (SMulHomClass.toFunLike.{max (max u2 u3) u4, u1, max u2 u4, max (max u2 u3) u4} (LinearEquiv.{u1, u1, max u2 u4, max u2 u3 u4} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u4, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u3 u4, u2} R R S (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (SMulZeroClass.toSMul.{u1, max u2 u4} S (X -> M) (AddMonoid.toZero.{max u2 u4} (X -> M) (AddCommMonoid.toAddMonoid.{max u2 u4} (X -> M) (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)))) (DistribSMul.toSMulZeroClass.{u1, max u2 u4} S (X -> M) (AddMonoid.toAddZeroClass.{max u2 u4} (X -> M) (AddCommMonoid.toAddMonoid.{max u2 u4} (X -> M) (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)))) (DistribMulAction.toDistribSMul.{u1, max u2 u4} S (X -> M) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max u2 u4} (X -> M) (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3))) (Module.toDistribMulAction.{u1, max u2 u4} S (X -> M) _inst_2 (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (Pi.module.{u4, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9)))))) (SMulZeroClass.toSMul.{u1, max (max u2 u3) u4} S (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddMonoid.toZero.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u3) u4} S (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddMonoid.toAddZeroClass.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u3) u4} S (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u2 u3) u4} S (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) _inst_2 (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u3 u4, u2} R R S (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u3) u4, u1, max u2 u4, max (max u2 u3) u4} (LinearEquiv.{u1, u1, max u2 u4, max u2 u3 u4} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u4, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u3 u4, u2} R R S (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max u2 u4} (X -> M) (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Module.toDistribMulAction.{u1, max u2 u4} S (X -> M) _inst_2 (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (Pi.module.{u4, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9))) (Module.toDistribMulAction.{u1, max (max u2 u3) u4} S (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R 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(RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (Pi.addZeroClass.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5047 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (AddMonoid.toAddZeroClass.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (AddEquiv.instAddEquivClassAddEquiv.{max u2 u4, max (max u2 u3) u4} (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (Pi.instAdd.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5047 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (LinearMap.instAddLinearMap.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) (Finsupp.lift.{u2, u3, u4} M R _inst_1 _inst_3 _inst_4 X) f) x)
+ forall (M : Type.{u2}) (R : Type.{u3}) (S : Type.{u1}) [_inst_1 : Semiring.{u3} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (X : Type.{u4}) [_inst_9 : Module.{u1, u2} S M _inst_2 _inst_3] [_inst_10 : SMulCommClass.{u3, u1, u2} R S M (SMulZeroClass.toSMul.{u3, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u2} R M (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} S M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} S M (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u1, u2} S M _inst_2 _inst_3 _inst_9))))] (f : X -> M) (x : Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) => M) x) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : X -> M) => LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) f) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (fun (_x : Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u2) (succ u4), max (max (succ u2) (succ u3)) (succ u4)} (LinearEquiv.{u1, u1, max u2 u4, max u2 u3 u4} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_2 _inst_9 _inst_10)) (X -> M) (fun (_x : X -> M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : X -> M) => LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) _x) (SMulHomClass.toFunLike.{max (max u2 u3) u4, u1, max u2 u4, max (max u2 u3) u4} (LinearEquiv.{u1, u1, max u2 u4, max u2 u3 u4} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u4, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u3 u4, u2} R R S (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (SMulZeroClass.toSMul.{u1, max u2 u4} S (X -> M) (AddMonoid.toZero.{max u2 u4} (X -> M) (AddCommMonoid.toAddMonoid.{max u2 u4} (X -> M) (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)))) (DistribSMul.toSMulZeroClass.{u1, max u2 u4} S (X -> M) (AddMonoid.toAddZeroClass.{max u2 u4} (X -> M) (AddCommMonoid.toAddMonoid.{max u2 u4} (X -> M) (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)))) (DistribMulAction.toDistribSMul.{u1, max u2 u4} S (X -> M) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max u2 u4} (X -> M) (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3))) (Module.toDistribMulAction.{u1, max u2 u4} S (X -> M) _inst_2 (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (Pi.module.{u4, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9)))))) (SMulZeroClass.toSMul.{u1, max (max u2 u3) u4} S (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddMonoid.toZero.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u3) u4} S (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddMonoid.toAddZeroClass.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u3) u4} S (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u2 u3) u4} S (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) _inst_2 (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u3 u4, u2} R R S (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u3) u4, u1, max u2 u4, max (max u2 u3) u4} (LinearEquiv.{u1, u1, max u2 u4, max u2 u3 u4} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u4, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u3 u4, u2} R R S (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max u2 u4} (X -> M) (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Module.toDistribMulAction.{u1, max u2 u4} S (X -> M) _inst_2 (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (Pi.module.{u4, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9))) (Module.toDistribMulAction.{u1, max (max u2 u3) u4} S (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) _inst_2 (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u3 u4, u2} R R S (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max u2 u4, max (max u2 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (AddEquiv.instAddEquivClassAddEquiv.{max u2 u4, max (max u2 u3) u4} (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R 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(Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) (Finsupp.lift.{u2, u3, u4} M R _inst_1 _inst_3 _inst_4 X) f) x)
Case conversion may be inaccurate. Consider using '#align finsupp.llift_apply Finsupp.llift_applyₓ'. -/
@[simp]
theorem llift_apply (f : X → M) (x : X →₀ R) : llift M R S X f x = lift M R X f x :=
@@ -1318,7 +1318,7 @@ protected def domLCongr {α₁ α₂ : Type _} (e : α₁ ≃ α₂) : (α₁
lean 3 declaration is
forall {M : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {α₁ : Type.{u3}} {α₂ : Type.{u4}} (e : Equiv.{succ u3, succ u4} α₁ α₂) (v : Finsupp.{u3, u1} α₁ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))), Eq.{max (succ u4) (succ u1)} (Finsupp.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (coeFn.{max (succ (max u3 u1)) (succ (max u4 u1)), max (succ (max u3 u1)) (succ (max u4 u1))} (LinearEquiv.{u2, u2, max u3 u1, max u4 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (Finsupp.{u3, u1} α₁ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.addCommMonoid.{u3, u1} α₁ M _inst_3) (Finsupp.addCommMonoid.{u4, u1} α₂ M _inst_3) (Finsupp.module.{u3, u1, u2} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u1, u2} α₂ M R _inst_1 _inst_3 _inst_4)) (fun (_x : LinearEquiv.{u2, u2, max u3 u1, max u4 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (Finsupp.{u3, u1} α₁ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.addCommMonoid.{u3, u1} α₁ M _inst_3) (Finsupp.addCommMonoid.{u4, u1} α₂ M _inst_3) 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(AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.add.{u3, u1} α₁ M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Finsupp.add.{u4, u1} α₂ M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) => (Finsupp.{u3, u1} α₁ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) -> (Finsupp.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (AddEquiv.hasCoeToFun.{max u3 u1, max u4 u1} (Finsupp.{u3, u1} α₁ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.add.{u3, u1} α₁ M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Finsupp.add.{u4, u1} α₂ M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.domCongr.{u3, u4, u1} α₁ α₂ M _inst_3 e) v)
but is expected to have type
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u2} α₁ α₂ M _inst_3 e) v)
Case conversion may be inaccurate. Consider using '#align finsupp.dom_lcongr_apply Finsupp.domLCongr_applyₓ'. -/
@[simp]
theorem domLCongr_apply {α₁ : Type _} {α₂ : Type _} (e : α₁ ≃ α₂) (v : α₁ →₀ M) :
mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee
@@ -212,50 +212,50 @@ theorem ker_lsingle (a : α) : (lsingle a : M →ₗ[R] α →₀ M).ker = ⊥ :
/- warning: finsupp.lsingle_range_le_ker_lapply -> Finsupp.lsingle_range_le_ker_lapply is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α) (t : Set.{u1} α), (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) s t) -> (LE.le.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toLE.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))))) (supᵢ.{max u1 u2, succ u1} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => supᵢ.{max u1 u2, 0} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LinearMap.range.{u3, u3, u2, max u1 u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u3, u3, u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R _inst_1) (Finsupp.lsingle.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a)))) (infᵢ.{max u1 u2, succ u1} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasInf.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) α (fun (a : α) => infᵢ.{max u1 u2, 0} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasInf.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a t) => LinearMap.ker.{u3, u3, max u1 u2, u2, max u1 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4) (LinearMap.semilinearMapClass.{u3, u3, max u1 u2, u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lapply.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a)))))
+ forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α) (t : Set.{u1} α), (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) s t) -> (LE.le.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toLE.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))))) (iSup.{max u1 u2, succ u1} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => iSup.{max u1 u2, 0} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LinearMap.range.{u3, u3, u2, max u1 u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u3, u3, u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R _inst_1) (Finsupp.lsingle.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a)))) (iInf.{max u1 u2, succ u1} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasInf.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) α (fun (a : α) => iInf.{max u1 u2, 0} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasInf.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a t) => LinearMap.ker.{u3, u3, max u1 u2, u2, max u1 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4) (LinearMap.semilinearMapClass.{u3, u3, max u1 u2, u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lapply.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a)))))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (t : Set.{u3} α), (Disjoint.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} α) (Preorder.toLE.{u3} (Set.{u3} α) (PartialOrder.toPreorder.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) s t) -> (LE.le.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toLE.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))))) (supᵢ.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => supᵢ.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) (fun (H : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a)))) (infᵢ.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) α (fun (a : α) => infᵢ.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a t) (fun (H : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a t) => LinearMap.ker.{u1, u1, max u3 u2, u2, max u3 u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u3 u2, u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lapply.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a)))))
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (t : Set.{u3} α), (Disjoint.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} α) (Preorder.toLE.{u3} (Set.{u3} α) (PartialOrder.toPreorder.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) s t) -> (LE.le.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toLE.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))))) (iSup.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => iSup.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) (fun (H : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a)))) (iInf.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) α (fun (a : α) => iInf.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a t) (fun (H : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a t) => LinearMap.ker.{u1, u1, max u3 u2, u2, max u3 u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u3 u2, u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lapply.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a)))))
Case conversion may be inaccurate. Consider using '#align finsupp.lsingle_range_le_ker_lapply Finsupp.lsingle_range_le_ker_lapplyₓ'. -/
theorem lsingle_range_le_ker_lapply (s t : Set α) (h : Disjoint s t) :
(⨆ a ∈ s, (lsingle a : M →ₗ[R] α →₀ M).range) ≤ ⨅ a ∈ t, ker (lapply a : (α →₀ M) →ₗ[R] M) :=
by
- refine' supᵢ_le fun a₁ => supᵢ_le fun h₁ => range_le_iff_comap.2 _
+ refine' iSup_le fun a₁ => iSup_le fun h₁ => range_le_iff_comap.2 _
simp only [(ker_comp _ _).symm, eq_top_iff, SetLike.le_def, mem_ker, comap_infi, mem_infi]
intro b hb a₂ h₂
have : a₁ ≠ a₂ := fun eq => h.le_bot ⟨h₁, Eq.symm ▸ h₂⟩
exact single_eq_of_ne this
#align finsupp.lsingle_range_le_ker_lapply Finsupp.lsingle_range_le_ker_lapply
-/- warning: finsupp.infi_ker_lapply_le_bot -> Finsupp.infᵢ_ker_lapply_le_bot is a dubious translation:
+/- warning: finsupp.infi_ker_lapply_le_bot -> Finsupp.iInf_ker_lapply_le_bot is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], LE.le.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toLE.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))))) (infᵢ.{max u1 u2, succ u1} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasInf.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) α (fun (a : α) => LinearMap.ker.{u3, u3, max u1 u2, u2, max u1 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4) (LinearMap.semilinearMapClass.{u3, u3, max u1 u2, u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lapply.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a))) (Bot.bot.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasBot.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))
+ forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], LE.le.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toLE.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))))) (iInf.{max u1 u2, succ u1} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasInf.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) α (fun (a : α) => LinearMap.ker.{u3, u3, max u1 u2, u2, max u1 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4) (LinearMap.semilinearMapClass.{u3, u3, max u1 u2, u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lapply.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a))) (Bot.bot.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasBot.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], LE.le.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toLE.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))))) (infᵢ.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) α (fun (a : α) => LinearMap.ker.{u1, u1, max u3 u2, u2, max u3 u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u3 u2, u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lapply.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a))) (Bot.bot.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instBotSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))
-Case conversion may be inaccurate. Consider using '#align finsupp.infi_ker_lapply_le_bot Finsupp.infᵢ_ker_lapply_le_botₓ'. -/
-theorem infᵢ_ker_lapply_le_bot : (⨅ a, ker (lapply a : (α →₀ M) →ₗ[R] M)) ≤ ⊥ :=
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], LE.le.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toLE.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))))) (iInf.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) α (fun (a : α) => LinearMap.ker.{u1, u1, max u3 u2, u2, max u3 u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u3 u2, u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lapply.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a))) (Bot.bot.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instBotSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))
+Case conversion may be inaccurate. Consider using '#align finsupp.infi_ker_lapply_le_bot Finsupp.iInf_ker_lapply_le_botₓ'. -/
+theorem iInf_ker_lapply_le_bot : (⨅ a, ker (lapply a : (α →₀ M) →ₗ[R] M)) ≤ ⊥ :=
by
simp only [SetLike.le_def, mem_infi, mem_ker, mem_bot, lapply_apply]
exact fun a h => Finsupp.ext h
-#align finsupp.infi_ker_lapply_le_bot Finsupp.infᵢ_ker_lapply_le_bot
+#align finsupp.infi_ker_lapply_le_bot Finsupp.iInf_ker_lapply_le_bot
-/- warning: finsupp.supr_lsingle_range -> Finsupp.supᵢ_lsingle_range is a dubious translation:
+/- warning: finsupp.supr_lsingle_range -> Finsupp.iSup_lsingle_range is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], Eq.{succ (max u1 u2)} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (supᵢ.{max u1 u2, succ u1} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => LinearMap.range.{u3, u3, u2, max u1 u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u3, u3, u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R _inst_1) (Finsupp.lsingle.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a))) (Top.top.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasTop.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))
+ forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], Eq.{succ (max u1 u2)} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (iSup.{max u1 u2, succ u1} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => LinearMap.range.{u3, u3, u2, max u1 u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u3, u3, u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R _inst_1) (Finsupp.lsingle.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a))) (Top.top.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasTop.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (supᵢ.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a))) (Top.top.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instTopSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))
-Case conversion may be inaccurate. Consider using '#align finsupp.supr_lsingle_range Finsupp.supᵢ_lsingle_rangeₓ'. -/
-theorem supᵢ_lsingle_range : (⨆ a, (lsingle a : M →ₗ[R] α →₀ M).range) = ⊤ :=
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (iSup.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a))) (Top.top.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instTopSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))
+Case conversion may be inaccurate. Consider using '#align finsupp.supr_lsingle_range Finsupp.iSup_lsingle_rangeₓ'. -/
+theorem iSup_lsingle_range : (⨆ a, (lsingle a : M →ₗ[R] α →₀ M).range) = ⊤ :=
by
refine' eq_top_iff.2 <| SetLike.le_def.2 fun f _ => _
rw [← sum_single f]
- exact sum_mem fun a ha => Submodule.mem_supᵢ_of_mem a ⟨_, rfl⟩
-#align finsupp.supr_lsingle_range Finsupp.supᵢ_lsingle_range
+ exact sum_mem fun a ha => Submodule.mem_iSup_of_mem a ⟨_, rfl⟩
+#align finsupp.supr_lsingle_range Finsupp.iSup_lsingle_range
/- warning: finsupp.disjoint_lsingle_lsingle -> Finsupp.disjoint_lsingle_lsingle is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α) (t : Set.{u1} α), (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) s t) -> (Disjoint.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) (Submodule.orderBot.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (supᵢ.{max u1 u2, succ u1} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => supᵢ.{max u1 u2, 0} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LinearMap.range.{u3, u3, u2, max u1 u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u3, u3, u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R _inst_1) (Finsupp.lsingle.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a)))) (supᵢ.{max u1 u2, succ u1} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => supᵢ.{max u1 u2, 0} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a t) => LinearMap.range.{u3, u3, u2, max u1 u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u3, u3, u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R _inst_1) (Finsupp.lsingle.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a)))))
+ forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α) (t : Set.{u1} α), (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) s t) -> (Disjoint.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) (Submodule.orderBot.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (iSup.{max u1 u2, succ u1} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => iSup.{max u1 u2, 0} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LinearMap.range.{u3, u3, u2, max u1 u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u3, u3, u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R _inst_1) (Finsupp.lsingle.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a)))) (iSup.{max u1 u2, succ u1} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => iSup.{max u1 u2, 0} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a t) => LinearMap.range.{u3, u3, u2, max u1 u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u3, u3, u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R _inst_1) (Finsupp.lsingle.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a)))))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (t : Set.{u3} α), (Disjoint.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} α) (Preorder.toLE.{u3} (Set.{u3} α) (PartialOrder.toPreorder.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) s t) -> (Disjoint.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (supᵢ.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => supᵢ.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) (fun (H : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a)))) (supᵢ.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => supᵢ.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a t) (fun (H : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a t) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a)))))
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (t : Set.{u3} α), (Disjoint.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} α) (Preorder.toLE.{u3} (Set.{u3} α) (PartialOrder.toPreorder.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) s t) -> (Disjoint.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (iSup.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => iSup.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) (fun (H : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a)))) (iSup.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => iSup.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a t) (fun (H : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a t) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a)))))
Case conversion may be inaccurate. Consider using '#align finsupp.disjoint_lsingle_lsingle Finsupp.disjoint_lsingle_lsingleₓ'. -/
theorem disjoint_lsingle_lsingle (s t : Set α) (hs : Disjoint s t) :
Disjoint (⨆ a ∈ s, (lsingle a : M →ₗ[R] α →₀ M).range)
@@ -266,13 +266,13 @@ theorem disjoint_lsingle_lsingle (s t : Set α) (hs : Disjoint s t) :
(lsingle_range_le_ker_lapply _ _ <| disjoint_compl_right))
_
rw [disjoint_iff_inf_le]
- refine' le_trans (le_infᵢ fun i => _) infi_ker_lapply_le_bot
+ refine' le_trans (le_iInf fun i => _) infi_ker_lapply_le_bot
classical
by_cases his : i ∈ s
· by_cases hit : i ∈ t
· exact (hs.le_bot ⟨his, hit⟩).elim
- exact inf_le_of_right_le (infᵢ_le_of_le i <| infᵢ_le _ hit)
- exact inf_le_of_left_le (infᵢ_le_of_le i <| infᵢ_le _ his)
+ exact inf_le_of_right_le (iInf_le_of_le i <| iInf_le _ hit)
+ exact inf_le_of_left_le (iInf_le_of_le i <| iInf_le _ his)
#align finsupp.disjoint_lsingle_lsingle Finsupp.disjoint_lsingle_lsingle
/- warning: finsupp.span_single_image -> Finsupp.span_single_image is a dubious translation:
@@ -466,16 +466,16 @@ theorem supported_univ : supported M R (Set.univ : Set α) = ⊤ :=
eq_top_iff.2 fun l _ => Set.subset_univ _
#align finsupp.supported_univ Finsupp.supported_univ
-/- warning: finsupp.supported_Union -> Finsupp.supported_unionᵢ is a dubious translation:
+/- warning: finsupp.supported_Union -> Finsupp.supported_iUnion is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {δ : Type.{u4}} (s : δ -> (Set.{u1} α)), Eq.{succ (max u1 u2)} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (Set.unionᵢ.{u1, succ u4} α δ (fun (i : δ) => s i))) (supᵢ.{max u1 u2, succ u4} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) δ (fun (i : δ) => Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (s i)))
+ forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {δ : Type.{u4}} (s : δ -> (Set.{u1} α)), Eq.{succ (max u1 u2)} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (Set.iUnion.{u1, succ u4} α δ (fun (i : δ) => s i))) (iSup.{max u1 u2, succ u4} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) δ (fun (i : δ) => Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (s i)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {δ : Type.{u4}} (s : δ -> (Set.{u3} α)), Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (Set.unionᵢ.{u3, succ u4} α δ (fun (i : δ) => s i))) (supᵢ.{max u2 u3, succ u4} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) δ (fun (i : δ) => Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (s i)))
-Case conversion may be inaccurate. Consider using '#align finsupp.supported_Union Finsupp.supported_unionᵢₓ'. -/
-theorem supported_unionᵢ {δ : Type _} (s : δ → Set α) :
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {δ : Type.{u4}} (s : δ -> (Set.{u3} α)), Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (Set.iUnion.{u3, succ u4} α δ (fun (i : δ) => s i))) (iSup.{max u2 u3, succ u4} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) δ (fun (i : δ) => Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (s i)))
+Case conversion may be inaccurate. Consider using '#align finsupp.supported_Union Finsupp.supported_iUnionₓ'. -/
+theorem supported_iUnion {δ : Type _} (s : δ → Set α) :
supported M R (⋃ i, s i) = ⨆ i, supported M R (s i) :=
by
- refine' le_antisymm _ (supᵢ_le fun i => supported_mono <| Set.subset_unionᵢ _ _)
+ refine' le_antisymm _ (iSup_le fun i => supported_mono <| Set.subset_iUnion _ _)
haveI := Classical.decPred fun x => x ∈ ⋃ i, s i
suffices
((Submodule.subtype _).comp (restrict_dom M R (⋃ i, s i))).range ≤ ⨆ i, supported M R (s i) by
@@ -487,8 +487,8 @@ theorem supported_unionᵢ {δ : Type _} (s : δ → Set α) :
refine' fun x a l hl a0 => add_mem _
by_cases ∃ i, x ∈ s i <;> simp [h]
· cases' h with i hi
- exact le_supᵢ (fun i => supported M R (s i)) i (single_mem_supported R _ hi)
-#align finsupp.supported_Union Finsupp.supported_unionᵢ
+ exact le_iSup (fun i => supported M R (s i)) i (single_mem_supported R _ hi)
+#align finsupp.supported_Union Finsupp.supported_iUnion
/- warning: finsupp.supported_union -> Finsupp.supported_union is a dubious translation:
lean 3 declaration is
@@ -497,19 +497,19 @@ but is expected to have type
forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (t : Set.{u3} α), Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (Union.union.{u3} (Set.{u3} α) (Set.instUnionSet.{u3} α) s t)) (Sup.sup.{max u2 u3} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SemilatticeSup.toSup.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Lattice.toSemilatticeSup.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toLattice.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))))) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 t))
Case conversion may be inaccurate. Consider using '#align finsupp.supported_union Finsupp.supported_unionₓ'. -/
theorem supported_union (s t : Set α) : supported M R (s ∪ t) = supported M R s ⊔ supported M R t :=
- by erw [Set.union_eq_unionᵢ, supported_Union, supᵢ_bool_eq] <;> rfl
+ by erw [Set.union_eq_iUnion, supported_Union, iSup_bool_eq] <;> rfl
#align finsupp.supported_union Finsupp.supported_union
-/- warning: finsupp.supported_Inter -> Finsupp.supported_interᵢ is a dubious translation:
+/- warning: finsupp.supported_Inter -> Finsupp.supported_iInter is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {ι : Type.{u4}} (s : ι -> (Set.{u1} α)), Eq.{succ (max u1 u2)} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (Set.interᵢ.{u1, succ u4} α ι (fun (i : ι) => s i))) (infᵢ.{max u1 u2, succ u4} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasInf.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) ι (fun (i : ι) => Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (s i)))
+ forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {ι : Type.{u4}} (s : ι -> (Set.{u1} α)), Eq.{succ (max u1 u2)} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (Set.iInter.{u1, succ u4} α ι (fun (i : ι) => s i))) (iInf.{max u1 u2, succ u4} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasInf.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) ι (fun (i : ι) => Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (s i)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {ι : Type.{u4}} (s : ι -> (Set.{u3} α)), Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (Set.interᵢ.{u3, succ u4} α ι (fun (i : ι) => s i))) (infᵢ.{max u2 u3, succ u4} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) ι (fun (i : ι) => Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (s i)))
-Case conversion may be inaccurate. Consider using '#align finsupp.supported_Inter Finsupp.supported_interᵢₓ'. -/
-theorem supported_interᵢ {ι : Type _} (s : ι → Set α) :
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {ι : Type.{u4}} (s : ι -> (Set.{u3} α)), Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (Set.iInter.{u3, succ u4} α ι (fun (i : ι) => s i))) (iInf.{max u2 u3, succ u4} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) ι (fun (i : ι) => Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (s i)))
+Case conversion may be inaccurate. Consider using '#align finsupp.supported_Inter Finsupp.supported_iInterₓ'. -/
+theorem supported_iInter {ι : Type _} (s : ι → Set α) :
supported M R (⋂ i, s i) = ⨅ i, supported M R (s i) :=
Submodule.ext fun x => by simp [mem_supported, subset_Inter_iff]
-#align finsupp.supported_Inter Finsupp.supported_interᵢ
+#align finsupp.supported_Inter Finsupp.supported_iInter
/- warning: finsupp.supported_inter -> Finsupp.supported_inter is a dubious translation:
lean 3 declaration is
@@ -518,7 +518,7 @@ but is expected to have type
forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (t : Set.{u3} α), Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (Inter.inter.{u3} (Set.{u3} α) (Set.instInterSet.{u3} α) s t)) (Inf.inf.{max u2 u3} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instInfSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 t))
Case conversion may be inaccurate. Consider using '#align finsupp.supported_inter Finsupp.supported_interₓ'. -/
theorem supported_inter (s t : Set α) : supported M R (s ∩ t) = supported M R s ⊓ supported M R t :=
- by rw [Set.inter_eq_interᵢ, supported_Inter, infᵢ_bool_eq] <;> rfl
+ by rw [Set.inter_eq_iInter, supported_Inter, iInf_bool_eq] <;> rfl
#align finsupp.supported_inter Finsupp.supported_inter
/- warning: finsupp.disjoint_supported_supported -> Finsupp.disjoint_supported_supported is a dubious translation:
@@ -1954,34 +1954,34 @@ theorem LinearMap.map_finsupp_total (f : M →ₗ[R] N) {ι : Type _} {g : ι
simp only [Finsupp.total_apply, Finsupp.total_apply, Finsupp.sum, f.map_sum, f.map_smul]
#align linear_map.map_finsupp_total LinearMap.map_finsupp_total
-/- warning: submodule.exists_finset_of_mem_supr -> Submodule.exists_finset_of_mem_supᵢ is a dubious translation:
+/- warning: submodule.exists_finset_of_mem_supr -> Submodule.exists_finset_of_mem_iSup is a dubious translation:
lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Type.{u3}} (p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) {m : M}, (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m (supᵢ.{u2, succ u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) -> (Exists.{succ u3} (Finset.{u3} ι) (fun (s : Finset.{u3} ι) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m (supᵢ.{u2, succ u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => supᵢ.{u2, 0} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) (fun (H : Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) => p i)))))
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Type.{u3}} (p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) {m : M}, (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m (iSup.{u2, succ u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) -> (Exists.{succ u3} (Finset.{u3} ι) (fun (s : Finset.{u3} ι) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m (iSup.{u2, succ u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => iSup.{u2, 0} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) (fun (H : Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) => p i)))))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Type.{u3}} (p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) {m : M}, (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m (supᵢ.{u1, succ u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) -> (Exists.{succ u3} (Finset.{u3} ι) (fun (s : Finset.{u3} ι) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m (supᵢ.{u1, succ u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => supᵢ.{u1, 0} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) (fun (H : Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) => p i)))))
-Case conversion may be inaccurate. Consider using '#align submodule.exists_finset_of_mem_supr Submodule.exists_finset_of_mem_supᵢₓ'. -/
-theorem Submodule.exists_finset_of_mem_supᵢ {ι : Sort _} (p : ι → Submodule R M) {m : M}
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Type.{u3}} (p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) {m : M}, (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m (iSup.{u1, succ u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) -> (Exists.{succ u3} (Finset.{u3} ι) (fun (s : Finset.{u3} ι) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m (iSup.{u1, succ u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => iSup.{u1, 0} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) (fun (H : Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) => p i)))))
+Case conversion may be inaccurate. Consider using '#align submodule.exists_finset_of_mem_supr Submodule.exists_finset_of_mem_iSupₓ'. -/
+theorem Submodule.exists_finset_of_mem_iSup {ι : Sort _} (p : ι → Submodule R M) {m : M}
(hm : m ∈ ⨆ i, p i) : ∃ s : Finset ι, m ∈ ⨆ i ∈ s, p i :=
by
have :=
- CompleteLattice.IsCompactElement.exists_finset_of_le_supᵢ (Submodule R M)
+ CompleteLattice.IsCompactElement.exists_finset_of_le_iSup (Submodule R M)
(Submodule.singleton_span_isCompactElement m) p
simp only [Submodule.span_singleton_le_iff_mem] at this
exact this hm
-#align submodule.exists_finset_of_mem_supr Submodule.exists_finset_of_mem_supᵢ
+#align submodule.exists_finset_of_mem_supr Submodule.exists_finset_of_mem_iSup
-/- warning: submodule.mem_supr_iff_exists_finset -> Submodule.mem_supᵢ_iff_exists_finset is a dubious translation:
+/- warning: submodule.mem_supr_iff_exists_finset -> Submodule.mem_iSup_iff_exists_finset is a dubious translation:
lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Type.{u3}} {p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)} {m : M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m (supᵢ.{u2, succ u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) (Exists.{succ u3} (Finset.{u3} ι) (fun (s : Finset.{u3} ι) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m (supᵢ.{u2, succ u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => supᵢ.{u2, 0} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) (fun (H : Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) => p i)))))
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Type.{u3}} {p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)} {m : M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m (iSup.{u2, succ u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) (Exists.{succ u3} (Finset.{u3} ι) (fun (s : Finset.{u3} ι) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m (iSup.{u2, succ u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => iSup.{u2, 0} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) (fun (H : Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) => p i)))))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Type.{u3}} {p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)} {m : M}, Iff (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m (supᵢ.{u1, succ u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) (Exists.{succ u3} (Finset.{u3} ι) (fun (s : Finset.{u3} ι) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m (supᵢ.{u1, succ u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => supᵢ.{u1, 0} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) (fun (H : Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) => p i)))))
-Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_iff_exists_finset Submodule.mem_supᵢ_iff_exists_finsetₓ'. -/
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Type.{u3}} {p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)} {m : M}, Iff (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m (iSup.{u1, succ u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) (Exists.{succ u3} (Finset.{u3} ι) (fun (s : Finset.{u3} ι) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m (iSup.{u1, succ u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => iSup.{u1, 0} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) (fun (H : Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) => p i)))))
+Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_iff_exists_finset Submodule.mem_iSup_iff_exists_finsetₓ'. -/
/-- `submodule.exists_finset_of_mem_supr` as an `iff` -/
-theorem Submodule.mem_supᵢ_iff_exists_finset {ι : Sort _} {p : ι → Submodule R M} {m : M} :
+theorem Submodule.mem_iSup_iff_exists_finset {ι : Sort _} {p : ι → Submodule R M} {m : M} :
(m ∈ ⨆ i, p i) ↔ ∃ s : Finset ι, m ∈ ⨆ i ∈ s, p i :=
- ⟨Submodule.exists_finset_of_mem_supᵢ p, fun ⟨_, hs⟩ =>
- supᵢ_mono (fun i => (supᵢ_const_le : _ ≤ p i)) hs⟩
-#align submodule.mem_supr_iff_exists_finset Submodule.mem_supᵢ_iff_exists_finset
+ ⟨Submodule.exists_finset_of_mem_iSup p, fun ⟨_, hs⟩ =>
+ iSup_mono (fun i => (iSup_const_le : _ ≤ p i)) hs⟩
+#align submodule.mem_supr_iff_exists_finset Submodule.mem_iSup_iff_exists_finset
#print mem_span_finset /-
theorem mem_span_finset {s : Finset M} {x : M} :
mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab
@@ -2094,7 +2094,7 @@ theorem splittingOfFinsuppSurjective_injective (f : M →ₗ[R] α →₀ R) (s
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3)
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17133 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u1) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17133 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17133 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17133 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17133 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) _inst_3)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u1) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) _inst_3)
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective LinearMap.splittingOfFunOnFintypeSurjectiveₓ'. -/
-- See also `linear_map.splitting_of_finsupp_surjective`
/-- A surjective linear map to functions on a finite type has a splitting. -/
@@ -2108,7 +2108,7 @@ def splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R) (s
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Eq.{succ (max u3 u1)} (LinearMap.{u1, u1, max u3 u1, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (LinearMap.comp.{u1, u1, u1, max u3 u1, u2, max u3 u1} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomCompTriple.right_ids.{u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u1, max u3 u1} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17216 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), 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α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17216 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Eq.{max (succ u2) (succ u3)} (LinearMap.{u2, u2, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17133 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17216 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.comp.{u2, u2, u2, max u2 u3, u1, max u2 u3} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17133 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17216 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u2, max u2 u3} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17133 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17208 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17208 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17208 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17208 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Eq.{max (succ u2) (succ u3)} (LinearMap.{u2, u2, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17208 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.comp.{u2, u2, u2, max u2 u3, u1, max u2 u3} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17208 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u2, max u2 u3} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)))
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective_splits LinearMap.splittingOfFunOnFintypeSurjective_splitsₓ'. -/
theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : f.comp (splittingOfFunOnFintypeSurjective f s) = LinearMap.id :=
@@ -2124,7 +2124,7 @@ theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R]
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Function.LeftInverse.{max (succ u3) (succ u1), succ u2} (α -> R) M (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f) (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) (fun (_x : LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) => (α -> R) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, u2} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17348 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), 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α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17348 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Function.LeftInverse.{max (succ u2) (succ u3), succ u1} (α -> R) M (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17348 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17348 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17348 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17133 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17133 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17133 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17340 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), 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α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17340 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Function.LeftInverse.{max (succ u2) (succ u3), succ u1} (α -> R) M (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17340 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17340 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17340 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
Case conversion may be inaccurate. Consider using '#align linear_map.left_inverse_splitting_of_fun_on_fintype_surjective LinearMap.leftInverse_splittingOfFunOnFintypeSurjectiveₓ'. -/
theorem leftInverse_splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : LeftInverse f (splittingOfFunOnFintypeSurjective f s) := fun g =>
@@ -2135,7 +2135,7 @@ theorem leftInverse_splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Function.Injective.{max (succ u3) (succ u1), succ u2} (α -> R) M (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) (fun (_x : LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) => (α -> R) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, u2} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17407 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17407 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17407 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17407 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Function.Injective.{max (succ u2) (succ u3), succ u1} (α -> R) M (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17133 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17133 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17133 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17399 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17399 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17399 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17399 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Function.Injective.{max (succ u2) (succ u3), succ u1} (α -> R) M (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17125 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective_injective LinearMap.splittingOfFunOnFintypeSurjective_injectiveₓ'. -/
theorem splittingOfFunOnFintypeSurjective_injective [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : Injective (splittingOfFunOnFintypeSurjective f s) :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/8b8ba04e2f326f3f7cf24ad129beda58531ada61
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
! This file was ported from Lean 3 source module linear_algebra.finsupp
-! leanprover-community/mathlib commit 3dec44d0b621a174c56e994da4aae15ba60110a2
+! leanprover-community/mathlib commit 9d684a893c52e1d6692a504a118bfccbae04feeb
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -479,7 +479,7 @@ theorem supported_unionᵢ {δ : Type _} (s : δ → Set α) :
haveI := Classical.decPred fun x => x ∈ ⋃ i, s i
suffices
((Submodule.subtype _).comp (restrict_dom M R (⋃ i, s i))).range ≤ ⨆ i, supported M R (s i) by
- rwa [LinearMap.range_comp, range_restrict_dom, map_top, range_subtype] at this
+ rwa [LinearMap.range_comp, range_restrict_dom, Submodule.map_top, range_subtype] at this
rw [range_le_iff_comap, eq_top_iff]
rintro l ⟨⟩
apply Finsupp.induction l
@@ -1251,7 +1251,8 @@ Case conversion may be inaccurate. Consider using '#align finsupp.total_on_range
theorem totalOn_range (s : Set α) : (Finsupp.totalOn α M R v s).range = ⊤ :=
by
rw [Finsupp.totalOn, LinearMap.range_eq_map, LinearMap.map_codRestrict, ←
- LinearMap.range_le_iff_comap, range_subtype, map_top, LinearMap.range_comp, range_subtype]
+ LinearMap.range_le_iff_comap, range_subtype, Submodule.map_top, LinearMap.range_comp,
+ range_subtype]
exact (span_image_eq_map_total _ _).le
#align finsupp.total_on_range Finsupp.totalOn_range
mathlib commit https://github.com/leanprover-community/mathlib/commit/7e281deff072232a3c5b3e90034bd65dde396312
@@ -1791,7 +1791,7 @@ variable {S}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] {S : Type.{u4}} [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (f : α -> R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) => (α -> M) -> (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4)) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, max (max u1 u3) u2} S S (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) f) (Finset.sum.{u2, u1} M α _inst_3 (Finset.univ.{u1} α _inst_1) (fun (i : α) => SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (f i) (v i)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (f : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) f) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) v) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearMap.{u1, u1, max u3 u4, max u4 u3 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u3, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14557 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14557 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14557 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) f) (Finset.sum.{u4, u3} M α _inst_3 (Finset.univ.{u3} α _inst_1) (fun (i : α) => HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) (f i) (v i)))
+ forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (f : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) f) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) v) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearMap.{u1, u1, max u3 u4, max u4 u3 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u3, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) f) (Finset.sum.{u4, u3} M α _inst_3 (Finset.univ.{u3} α _inst_1) (fun (i : α) => HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) (f i) (v i)))
Case conversion may be inaccurate. Consider using '#align fintype.total_apply Fintype.total_applyₓ'. -/
theorem Fintype.total_apply (f) : Fintype.total R S v f = ∑ i, f i • v i :=
rfl
@@ -1801,7 +1801,7 @@ theorem Fintype.total_apply (f) : Fintype.total R S v f = ∑ i, f i • v i :=
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] {S : Type.{u4}} [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (i : α) (r : R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R 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(Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) (Pi.single.{u1, u3} α (fun (ᾰ : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u1} α a b)) (fun (i : α) => MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) i r)) (SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) r (v i))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (i : α) (r : R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) (Pi.single.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14557 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) (Pi.single.{u3, u2} α (fun (ᾰ : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) r (v i))
+ forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (i : α) (r : R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) (Pi.single.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) v) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearMap.{u1, u1, max u3 u4, max u4 u3 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u3, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) (Pi.single.{u3, u2} α (fun (ᾰ : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) r (v i))
Case conversion may be inaccurate. Consider using '#align fintype.total_apply_single Fintype.total_apply_singleₓ'. -/
@[simp]
theorem Fintype.total_apply_single (i : α) (r : R) :
@@ -1817,7 +1817,7 @@ variable (S)
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] (S : Type.{u4}) [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (x : α -> R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) => (α -> M) -> (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4)) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, max (max u1 u3) u2} S S (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) x)
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (x : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) => M) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (α -> R) (fun (a : α -> R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> R) => Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) a) (SMulHomClass.toFunLike.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (α -> R) (AddMonoid.toZero.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (α -> R) (AddMonoid.toAddZeroClass.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (α -> R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => 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(Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u3 u2, max u3 u2, max u3 u2} R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u3 u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R 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(Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R 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(Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (Finsupp.linearEquivFunOnFinite.{u2, u2, u3} R R α (Finite.of_fintype.{u3} α _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) _inst_2 (Semiring.toModule.{u2} R _inst_2))) x)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) (fun (i : α) => 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(fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearMap.{u1, u1, max u3 u4, max u4 u3 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u3, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14557 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14557 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14557 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) x)
+ forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (x : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) => M) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (α -> R) (fun (a : α -> R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> R) => Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) a) (SMulHomClass.toFunLike.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (α -> R) (AddMonoid.toZero.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (α -> R) (AddMonoid.toAddZeroClass.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (α -> R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u3 u2, max u3 u2, max u3 u2} R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) 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(a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (α -> R) (AddMonoid.toAddZeroClass.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (α -> R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u3 u2, max u3 u2, max u3 u2} R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u3 u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2)))))) (LinearEquiv.symm.{u2, u2, max u3 u2, max u3 u2} R R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (α -> R) _inst_2 _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R 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(fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) x)
Case conversion may be inaccurate. Consider using '#align finsupp.total_eq_fintype_total_apply Finsupp.total_eq_fintype_total_applyₓ'. -/
theorem Finsupp.total_eq_fintype_total_apply (x : α → R) :
Finsupp.total α M R v ((Finsupp.linearEquivFunOnFinite R R α).symm x) = Fintype.total R S v x :=
@@ -1833,7 +1833,7 @@ theorem Finsupp.total_eq_fintype_total_apply (x : α → R) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] (S : Type.{u4}) [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (LinearMap.comp.{u3, u3, u3, max u1 u3, max u1 u3, u2} R R R (α -> R) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))) M _inst_2 _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHomCompTriple.right_ids.{u3, u3} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Finsupp.total.{u1, u2, u3} α M R _inst_2 _inst_3 _inst_4 v) (LinearEquiv.toLinearMap.{u3, u3, max u1 u3, max u1 u3} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHomInvPair.ids.{u3} R _inst_2) (RingHomInvPair.ids.{u3} R _inst_2) (α -> R) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))))) (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Pi.Function.module.{u1, 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)
but is expected to have type
- forall {α : Type.{u4}} {M : Type.{u3}} (R : Type.{u2}) [_inst_1 : Fintype.{u4} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u3} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u3} R S M (SMulZeroClass.toSMul.{u2, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u2, u3} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u3} S M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u1, u3} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R 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Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomCompTriple.ids.{u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Finsupp.total.{u4, u3, u2} α M R _inst_2 _inst_3 _inst_4 v) (LinearEquiv.toLinearMap.{u2, u2, max u4 u2, max u4 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u4, u2} α R (AddMonoid.toZero.{u2} R 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(a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u4, u3} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u4 u2, u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u4, u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14557 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u4 u2, u3} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S 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+ forall {α : Type.{u4}} {M : Type.{u3}} (R : Type.{u2}) [_inst_1 : Fintype.{u4} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u3} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u3} R S M (SMulZeroClass.toSMul.{u2, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u2, u3} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u3} S M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u1, u3} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (LinearEquiv.symm.{u2, u2, max u4 u2, max u4 u2} R R (Finsupp.{u4, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (α -> R) _inst_2 _inst_2 (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R 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(Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u4, u3, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)
Case conversion may be inaccurate. Consider using '#align finsupp.total_eq_fintype_total Finsupp.total_eq_fintype_totalₓ'. -/
theorem Finsupp.total_eq_fintype_total :
(Finsupp.total α M R v).comp (Finsupp.linearEquivFunOnFinite R R α).symm.toLinearMap =
@@ -1847,7 +1847,7 @@ variable {S}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] {S : Type.{u4}} [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{succ u2} (Submodule.{u3, u2} R M _inst_2 _inst_3 _inst_4) (LinearMap.range.{u3, u3, max u1 u3, u2, max (max u1 u3) u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (LinearMap.semilinearMapClass.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (RingHomSurjective.ids.{u3} R _inst_2) (coeFn.{max (succ (max u1 u2)) (succ (max (max u1 u3) u2)), max (succ (max u1 u2)) (succ (max (max u1 u3) u2))} (LinearMap.{u4, u4, max u1 u2, max (max u1 u3) u2} S S _inst_5 _inst_5 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) (fun (_x : 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(Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) => (α -> M) -> (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4)) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, max (max u1 u3) u2} S S (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)) (Submodule.span.{u3, u2} R M _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u1} M α v))
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u4}} (R : Type.{u3}) [_inst_1 : Fintype.{u2} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u3, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u1, u4} R S M (SMulZeroClass.toSMul.{u3, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u4} R M (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u4} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u3, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{succ u4} (Submodule.{u3, u4} R M _inst_2 _inst_3 _inst_4) (LinearMap.range.{u3, u3, max u2 u3, u4, max (max u2 u4) u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) v) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (RingHomSurjective.ids.{u3} R _inst_2) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearMap.{u1, u1, max u2 u4, max u4 u2 u3} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u2, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14557 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.module.{u2, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14557 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u2 u3, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u2, max (max u3 u4) u2} S S (α -> M) (LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u2, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.module.{u2, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14557 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u2 u3, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u2, u4, u3, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)) (Submodule.span.{u3, u4} R M _inst_2 _inst_3 _inst_4 (Set.range.{u4, succ u2} M α v))
+ forall {α : Type.{u2}} {M : Type.{u4}} (R : Type.{u3}) [_inst_1 : Fintype.{u2} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u3, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u1, u4} R S M (SMulZeroClass.toSMul.{u3, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u4} R M (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u4} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u3, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{succ u4} (Submodule.{u3, u4} R M _inst_2 _inst_3 _inst_4) (LinearMap.range.{u3, u3, max u2 u3, u4, max (max u2 u4) u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) v) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (RingHomSurjective.ids.{u3} R _inst_2) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearMap.{u1, u1, max u2 u4, max u4 u2 u3} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u2, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun 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NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R 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(Pi.module.{u2, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u2 u3, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u2, u4, u3, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)) (Submodule.span.{u3, u4} R M _inst_2 _inst_3 _inst_4 (Set.range.{u4, succ u2} M α v))
Case conversion may be inaccurate. Consider using '#align fintype.range_total Fintype.range_totalₓ'. -/
@[simp]
theorem Fintype.range_total : (Fintype.total R S v).range = Submodule.span R (Set.range v) := by
@@ -2093,7 +2093,7 @@ theorem splittingOfFinsuppSurjective_injective (f : M →ₗ[R] α →₀ R) (s
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3)
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17132 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u1) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17132 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17132 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17132 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17132 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) _inst_3)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17133 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u1) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17133 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17133 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17133 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17133 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) _inst_3)
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective LinearMap.splittingOfFunOnFintypeSurjectiveₓ'. -/
-- See also `linear_map.splitting_of_finsupp_surjective`
/-- A surjective linear map to functions on a finite type has a splitting. -/
@@ -2107,7 +2107,7 @@ def splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R) (s
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Eq.{succ (max u3 u1)} (LinearMap.{u1, u1, max u3 u1, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (LinearMap.comp.{u1, u1, u1, max u3 u1, u2, max u3 u1} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomCompTriple.right_ids.{u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u1, max u3 u1} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17215 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), 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α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17215 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Eq.{max (succ u2) (succ u3)} (LinearMap.{u2, u2, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17132 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17215 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.comp.{u2, u2, u2, max u2 u3, u1, max u2 u3} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17132 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17215 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u2, max u2 u3} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17132 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17216 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17216 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17216 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17216 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Eq.{max (succ u2) (succ u3)} (LinearMap.{u2, u2, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17133 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17216 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.comp.{u2, u2, u2, max u2 u3, u1, max u2 u3} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17133 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17216 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u2, max u2 u3} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17133 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)))
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective_splits LinearMap.splittingOfFunOnFintypeSurjective_splitsₓ'. -/
theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : f.comp (splittingOfFunOnFintypeSurjective f s) = LinearMap.id :=
@@ -2123,7 +2123,7 @@ theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R]
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Function.LeftInverse.{max (succ u3) (succ u1), succ u2} (α -> R) M (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f) (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) (fun (_x : LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) => (α -> R) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, u2} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17347 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), 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R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17347 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17347 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17132 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17132 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17132 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17348 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), 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α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17348 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Function.LeftInverse.{max (succ u2) (succ u3), succ u1} (α -> R) M (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17348 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17133 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17133 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => 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Case conversion may be inaccurate. Consider using '#align linear_map.left_inverse_splitting_of_fun_on_fintype_surjective LinearMap.leftInverse_splittingOfFunOnFintypeSurjectiveₓ'. -/
theorem leftInverse_splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : LeftInverse f (splittingOfFunOnFintypeSurjective f s) := fun g =>
@@ -2134,7 +2134,7 @@ theorem leftInverse_splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Function.Injective.{max (succ u3) (succ u1), succ u2} (α -> R) M (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) (fun (_x : LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) => (α -> R) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, u2} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17406 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17406 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17406 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17406 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Function.Injective.{max (succ u2) (succ u3), succ u1} (α -> R) M (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17132 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17132 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17132 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17407 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17407 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17407 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17407 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Function.Injective.{max (succ u2) (succ u3), succ u1} (α -> R) M (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17133 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17133 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17133 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective_injective LinearMap.splittingOfFunOnFintypeSurjective_injectiveₓ'. -/
theorem splittingOfFunOnFintypeSurjective_injective [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : Injective (splittingOfFunOnFintypeSurjective f s) :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/7ebf83ed9c262adbf983ef64d5e8c2ae94b625f4
@@ -2093,7 +2093,7 @@ theorem splittingOfFinsuppSurjective_injective (f : M →ₗ[R] α →₀ R) (s
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3)
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17159 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u1) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17159 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17159 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17159 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17159 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) _inst_3)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17132 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u1) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17132 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17132 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17132 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17132 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) _inst_3)
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective LinearMap.splittingOfFunOnFintypeSurjectiveₓ'. -/
-- See also `linear_map.splitting_of_finsupp_surjective`
/-- A surjective linear map to functions on a finite type has a splitting. -/
@@ -2107,7 +2107,7 @@ def splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R) (s
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Eq.{succ (max u3 u1)} (LinearMap.{u1, u1, max u3 u1, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (LinearMap.comp.{u1, u1, u1, max u3 u1, u2, max u3 u1} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomCompTriple.right_ids.{u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u1, max u3 u1} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17242 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17242 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17242 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17242 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Eq.{max (succ u2) (succ u3)} (LinearMap.{u2, u2, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17159 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17242 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.comp.{u2, u2, u2, max u2 u3, u1, max u2 u3} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17159 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17242 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u2, max u2 u3} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17159 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17215 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17215 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17215 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17215 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Eq.{max (succ u2) (succ u3)} (LinearMap.{u2, u2, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17132 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17215 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.comp.{u2, u2, u2, max u2 u3, u1, max u2 u3} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17132 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17215 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u2, max u2 u3} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17132 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)))
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective_splits LinearMap.splittingOfFunOnFintypeSurjective_splitsₓ'. -/
theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : f.comp (splittingOfFunOnFintypeSurjective f s) = LinearMap.id :=
@@ -2123,7 +2123,7 @@ theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R]
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Function.LeftInverse.{max (succ u3) (succ u1), succ u2} (α -> R) M (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f) (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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but is expected to have type
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17159 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17159 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => 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+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17347 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), 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Case conversion may be inaccurate. Consider using '#align linear_map.left_inverse_splitting_of_fun_on_fintype_surjective LinearMap.leftInverse_splittingOfFunOnFintypeSurjectiveₓ'. -/
theorem leftInverse_splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : LeftInverse f (splittingOfFunOnFintypeSurjective f s) := fun g =>
@@ -2134,7 +2134,7 @@ theorem leftInverse_splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Function.Injective.{max (succ u3) (succ u1), succ u2} (α -> R) M (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) (fun (_x : LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) => (α -> R) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, u2} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17433 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17433 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17433 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17433 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Function.Injective.{max (succ u2) (succ u3), succ u1} (α -> R) M (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17159 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17159 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17159 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17406 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17406 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17406 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17406 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Function.Injective.{max (succ u2) (succ u3), succ u1} (α -> R) M (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17132 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17132 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17132 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective_injective LinearMap.splittingOfFunOnFintypeSurjective_injectiveₓ'. -/
theorem splittingOfFunOnFintypeSurjective_injective [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : Injective (splittingOfFunOnFintypeSurjective f s) :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/039ef89bef6e58b32b62898dd48e9d1a4312bb65
@@ -2093,7 +2093,7 @@ theorem splittingOfFinsuppSurjective_injective (f : M →ₗ[R] α →₀ R) (s
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3)
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17158 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u1) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17158 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17158 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17158 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17158 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) _inst_3)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17159 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u1) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17159 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17159 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17159 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17159 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) _inst_3)
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective LinearMap.splittingOfFunOnFintypeSurjectiveₓ'. -/
-- See also `linear_map.splitting_of_finsupp_surjective`
/-- A surjective linear map to functions on a finite type has a splitting. -/
@@ -2107,7 +2107,7 @@ def splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R) (s
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Eq.{succ (max u3 u1)} (LinearMap.{u1, u1, max u3 u1, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (LinearMap.comp.{u1, u1, u1, max u3 u1, u2, max u3 u1} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomCompTriple.right_ids.{u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u1, max u3 u1} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17241 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17241 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17241 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17241 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Eq.{max (succ u2) (succ u3)} (LinearMap.{u2, u2, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17158 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17241 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.comp.{u2, u2, u2, max u2 u3, u1, max u2 u3} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17158 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17241 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u2, max u2 u3} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17158 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17242 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17242 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17242 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17242 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Eq.{max (succ u2) (succ u3)} (LinearMap.{u2, u2, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17159 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17242 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.comp.{u2, u2, u2, max u2 u3, u1, max u2 u3} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17159 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17242 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u2, max u2 u3} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17159 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)))
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective_splits LinearMap.splittingOfFunOnFintypeSurjective_splitsₓ'. -/
theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : f.comp (splittingOfFunOnFintypeSurjective f s) = LinearMap.id :=
@@ -2123,7 +2123,7 @@ theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R]
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Function.LeftInverse.{max (succ u3) (succ u1), succ u2} (α -> R) M (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f) (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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but is expected to have type
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17158 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17158 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => 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+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17374 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), 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Case conversion may be inaccurate. Consider using '#align linear_map.left_inverse_splitting_of_fun_on_fintype_surjective LinearMap.leftInverse_splittingOfFunOnFintypeSurjectiveₓ'. -/
theorem leftInverse_splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : LeftInverse f (splittingOfFunOnFintypeSurjective f s) := fun g =>
@@ -2134,7 +2134,7 @@ theorem leftInverse_splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Function.Injective.{max (succ u3) (succ u1), succ u2} (α -> R) M (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) (fun (_x : LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) => (α -> R) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, u2} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17432 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17432 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17432 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17432 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Function.Injective.{max (succ u2) (succ u3), succ u1} (α -> R) M (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17158 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17158 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17158 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17433 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17433 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17433 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17433 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Function.Injective.{max (succ u2) (succ u3), succ u1} (α -> R) M (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17159 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17159 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17159 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective_injective LinearMap.splittingOfFunOnFintypeSurjective_injectiveₓ'. -/
theorem splittingOfFunOnFintypeSurjective_injective [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : Injective (splittingOfFunOnFintypeSurjective f s) :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/e05ead7993520a432bec94ac504842d90707ad63
@@ -1791,7 +1791,7 @@ variable {S}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] {S : Type.{u4}} [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (f : α -> R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R 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(Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) f) (Finset.sum.{u2, u1} M α _inst_3 (Finset.univ.{u1} α _inst_1) (fun (i : α) => SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (f i) (v i)))
but is expected to have type
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(MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (f : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) f) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R 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NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u3, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14461 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14461 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14461 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) f) (Finset.sum.{u4, u3} M α _inst_3 (Finset.univ.{u3} α _inst_1) (fun (i : α) => HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) (f i) (v i)))
+ forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (f : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) f) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) v) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearMap.{u1, u1, max u3 u4, max u4 u3 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u3, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14557 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14557 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14557 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) f) (Finset.sum.{u4, u3} M α _inst_3 (Finset.univ.{u3} α _inst_1) (fun (i : α) => HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) (f i) (v i)))
Case conversion may be inaccurate. Consider using '#align fintype.total_apply Fintype.total_applyₓ'. -/
theorem Fintype.total_apply (f) : Fintype.total R S v f = ∑ i, f i • v i :=
rfl
@@ -1801,7 +1801,7 @@ theorem Fintype.total_apply (f) : Fintype.total R S v f = ∑ i, f i • v i :=
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] {S : Type.{u4}} [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (i : α) (r : R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R 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(Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) (Pi.single.{u1, u3} α (fun (ᾰ : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u1} α a b)) (fun (i : α) => MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) i r)) (SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) r (v i))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (i : α) (r : R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) (Pi.single.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} 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_inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14461 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) (Pi.single.{u3, u2} α (fun (ᾰ : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) r (v i))
+ forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (i : α) (r : R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) (Pi.single.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) v) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearMap.{u1, u1, max u3 u4, max u4 u3 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14557 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) (Pi.single.{u3, u2} α (fun (ᾰ : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) r (v i))
Case conversion may be inaccurate. Consider using '#align fintype.total_apply_single Fintype.total_apply_singleₓ'. -/
@[simp]
theorem Fintype.total_apply_single (i : α) (r : R) :
@@ -1817,7 +1817,7 @@ variable (S)
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] (S : Type.{u4}) [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (x : α -> R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R 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u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Finsupp.total.{u1, u2, u3} α M R _inst_2 _inst_3 _inst_4 v) (coeFn.{succ (max u1 u3), succ (max u1 u3)} (LinearEquiv.{u3, u3, max u1 u3, max u1 u3} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHomInvPair.ids.{u3} R _inst_2) (RingHomInvPair.ids.{u3} R _inst_2) (α -> R) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R 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(Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) x)
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (x : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) => M) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (α -> R) (fun (a : α -> R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> R) => Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) a) (SMulHomClass.toFunLike.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R 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(Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (α -> R) (AddMonoid.toZero.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (α -> R) (AddMonoid.toAddZeroClass.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (α -> R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u3 u2, max u3 u2, max u3 u2} R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u3 u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2)))))) (LinearEquiv.symm.{u2, u2, max u3 u2, max u3 u2} R R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (α -> R) _inst_2 _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (Finsupp.linearEquivFunOnFinite.{u2, u2, u3} R R α (Finite.of_fintype.{u3} α _inst_1) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R 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(Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14461 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14461 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) x)
+ forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (x : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) => M) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (α -> R) (fun (a : α -> R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> R) => Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) a) (SMulHomClass.toFunLike.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (α -> R) (AddMonoid.toZero.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (α -> R) (AddMonoid.toAddZeroClass.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (α -> R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u3 u2, max u3 u2, max u3 u2} R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u3 u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R 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Case conversion may be inaccurate. Consider using '#align finsupp.total_eq_fintype_total_apply Finsupp.total_eq_fintype_total_applyₓ'. -/
theorem Finsupp.total_eq_fintype_total_apply (x : α → R) :
Finsupp.total α M R v ((Finsupp.linearEquivFunOnFinite R R α).symm x) = Fintype.total R S v x :=
@@ -1833,7 +1833,7 @@ theorem Finsupp.total_eq_fintype_total_apply (x : α → R) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] (S : Type.{u4}) [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (LinearMap.comp.{u3, u3, u3, max u1 u3, max u1 u3, u2} R R R (α -> R) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))) M _inst_2 _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHomCompTriple.right_ids.{u3, u3} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Finsupp.total.{u1, u2, u3} α M R _inst_2 _inst_3 _inst_4 v) (LinearEquiv.toLinearMap.{u3, u3, max u1 u3, max u1 u3} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHomInvPair.ids.{u3} R _inst_2) (RingHomInvPair.ids.{u3} R _inst_2) (α -> R) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))))) (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) (LinearEquiv.symm.{u3, u3, max u1 u3, max u1 u3} R R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))))) (α -> R) _inst_2 _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHomInvPair.ids.{u3} R _inst_2) (RingHomInvPair.ids.{u3} R _inst_2) (Finsupp.linearEquivFunOnFinite.{u3, u3, u1} R R α (Finite.of_fintype.{u1} α _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) _inst_2 (Semiring.toModule.{u3} R _inst_2))))) (coeFn.{max (succ (max u1 u2)) (succ (max (max u1 u3) u2)), max (succ (max u1 u2)) (succ (max (max u1 u3) u2))} (LinearMap.{u4, u4, max u1 u2, max (max u1 u3) u2} S S _inst_5 _inst_5 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4)) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, max (max u1 u3) u2} S S (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)
but is expected to have type
- forall {α : Type.{u4}} {M : Type.{u3}} (R : Type.{u2}) [_inst_1 : Fintype.{u4} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u3} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u3} R S M (SMulZeroClass.toSMul.{u2, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u2, u3} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u3} S M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u1, u3} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (LinearMap.comp.{u2, u2, u2, max u4 u2, max u4 u2, u3} R R R (α -> R) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) M _inst_2 _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomCompTriple.ids.{u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Finsupp.total.{u4, u3, u2} α M R _inst_2 _inst_3 _inst_4 v) (LinearEquiv.toLinearMap.{u2, u2, max u4 u2, max u4 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u4, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (LinearEquiv.symm.{u2, u2, max u4 u2, max u4 u2} R R (Finsupp.{u4, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (α -> R) _inst_2 _inst_2 (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (Finsupp.linearEquivFunOnFinite.{u2, u2, u4} R R α (Finite.of_fintype.{u4} α _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) _inst_2 (Semiring.toModule.{u2} R _inst_2))))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), max (max (succ u2) (succ u3)) (succ u4)} (LinearMap.{u1, u1, max u4 u3, max u3 u4 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u4, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14461 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u4 u2, u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u4, u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14461 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u4 u2, u3} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u4, max (max u2 u3) u4} S S (α -> M) (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u4, u3} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u4 u2, u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u4, u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14461 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u4 u2, u3} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u4, u3, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)
+ forall {α : Type.{u4}} {M : Type.{u3}} (R : Type.{u2}) [_inst_1 : Fintype.{u4} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u3} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u3} R S M (SMulZeroClass.toSMul.{u2, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u2, u3} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u3} S M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u1, u3} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (LinearMap.comp.{u2, u2, u2, max u4 u2, max u4 u2, u3} R R R (α -> R) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) M _inst_2 _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomCompTriple.ids.{u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Finsupp.total.{u4, u3, u2} α M R _inst_2 _inst_3 _inst_4 v) (LinearEquiv.toLinearMap.{u2, u2, max u4 u2, max u4 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u4, u2} α R (AddMonoid.toZero.{u2} R 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_inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u4, u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14557 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u4 u2, u3} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u4, u3, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)
Case conversion may be inaccurate. Consider using '#align finsupp.total_eq_fintype_total Finsupp.total_eq_fintype_totalₓ'. -/
theorem Finsupp.total_eq_fintype_total :
(Finsupp.total α M R v).comp (Finsupp.linearEquivFunOnFinite R R α).symm.toLinearMap =
@@ -1847,7 +1847,7 @@ variable {S}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] {S : Type.{u4}} [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{succ u2} (Submodule.{u3, u2} R M _inst_2 _inst_3 _inst_4) (LinearMap.range.{u3, u3, max u1 u3, u2, max (max u1 u3) u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (LinearMap.semilinearMapClass.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (RingHomSurjective.ids.{u3} R _inst_2) (coeFn.{max (succ (max u1 u2)) (succ (max (max u1 u3) u2)), max (succ (max u1 u2)) (succ (max (max u1 u3) u2))} (LinearMap.{u4, u4, max u1 u2, max (max u1 u3) u2} S S _inst_5 _inst_5 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) (fun (_x : LinearMap.{u4, u4, max u1 u2, max (max u1 u3) u2} S S _inst_5 _inst_5 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) => (α -> M) -> (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4)) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, max (max u1 u3) u2} S S (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)) (Submodule.span.{u3, u2} R M _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u1} M α v))
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u4}} (R : Type.{u3}) [_inst_1 : Fintype.{u2} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u3, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u1, u4} R S M (SMulZeroClass.toSMul.{u3, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u4} R M (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u4} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u3, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{succ u4} (Submodule.{u3, u4} R M _inst_2 _inst_3 _inst_4) (LinearMap.range.{u3, u3, max u2 u3, u4, max (max u2 u4) u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) v) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (RingHomSurjective.ids.{u3} R _inst_2) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearMap.{u1, u1, max u2 u4, max u4 u2 u3} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u2, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14461 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun 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(Pi.module.{u2, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14461 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u2 u3, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u2, u4, u3, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)) (Submodule.span.{u3, u4} R M _inst_2 _inst_3 _inst_4 (Set.range.{u4, succ u2} M α v))
+ forall {α : Type.{u2}} {M : Type.{u4}} (R : Type.{u3}) [_inst_1 : Fintype.{u2} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u3, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u1, u4} R S M (SMulZeroClass.toSMul.{u3, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u4} R M (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u4} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u3, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{succ u4} (Submodule.{u3, u4} R M _inst_2 _inst_3 _inst_4) (LinearMap.range.{u3, u3, max u2 u3, u4, max (max u2 u4) u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) v) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (RingHomSurjective.ids.{u3} R _inst_2) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearMap.{u1, u1, max u2 u4, max u4 u2 u3} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u2, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14557 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.module.{u2, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14557 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u2 u3, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u2, max (max u3 u4) u2} S S (α -> M) (LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u2, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.module.{u2, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14557 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u2 u3, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14569 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u2, u4, u3, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)) (Submodule.span.{u3, u4} R M _inst_2 _inst_3 _inst_4 (Set.range.{u4, succ u2} M α v))
Case conversion may be inaccurate. Consider using '#align fintype.range_total Fintype.range_totalₓ'. -/
@[simp]
theorem Fintype.range_total : (Fintype.total R S v).range = Submodule.span R (Set.range v) := by
@@ -2093,7 +2093,7 @@ theorem splittingOfFinsuppSurjective_injective (f : M →ₗ[R] α →₀ R) (s
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3)
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17062 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u1) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17062 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17062 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17062 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17062 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) _inst_3)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17158 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u1) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17158 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17158 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17158 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17158 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) _inst_3)
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective LinearMap.splittingOfFunOnFintypeSurjectiveₓ'. -/
-- See also `linear_map.splitting_of_finsupp_surjective`
/-- A surjective linear map to functions on a finite type has a splitting. -/
@@ -2107,7 +2107,7 @@ def splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R) (s
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Eq.{succ (max u3 u1)} (LinearMap.{u1, u1, max u3 u1, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (LinearMap.comp.{u1, u1, u1, max u3 u1, u2, max u3 u1} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomCompTriple.right_ids.{u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u1, max u3 u1} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17145 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17145 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17145 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17145 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Eq.{max (succ u2) (succ u3)} (LinearMap.{u2, u2, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17062 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17145 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.comp.{u2, u2, u2, max u2 u3, u1, max u2 u3} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17062 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17145 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u2, max u2 u3} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17062 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17241 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17241 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17241 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17241 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Eq.{max (succ u2) (succ u3)} (LinearMap.{u2, u2, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17158 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17241 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.comp.{u2, u2, u2, max u2 u3, u1, max u2 u3} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17158 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17241 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u2, max u2 u3} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17158 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)))
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective_splits LinearMap.splittingOfFunOnFintypeSurjective_splitsₓ'. -/
theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : f.comp (splittingOfFunOnFintypeSurjective f s) = LinearMap.id :=
@@ -2123,7 +2123,7 @@ theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R]
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Function.LeftInverse.{max (succ u3) (succ u1), succ u2} (α -> R) M (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f) (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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but is expected to have type
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17062 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17062 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => 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+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17373 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), 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Case conversion may be inaccurate. Consider using '#align linear_map.left_inverse_splitting_of_fun_on_fintype_surjective LinearMap.leftInverse_splittingOfFunOnFintypeSurjectiveₓ'. -/
theorem leftInverse_splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : LeftInverse f (splittingOfFunOnFintypeSurjective f s) := fun g =>
@@ -2134,7 +2134,7 @@ theorem leftInverse_splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Function.Injective.{max (succ u3) (succ u1), succ u2} (α -> R) M (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) (fun (_x : LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) => (α -> R) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, u2} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17336 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17336 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17336 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17336 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Function.Injective.{max (succ u2) (succ u3), succ u1} (α -> R) M (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17062 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17062 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17062 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17432 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17432 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17432 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17432 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Function.Injective.{max (succ u2) (succ u3), succ u1} (α -> R) M (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17158 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17158 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17158 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective_injective LinearMap.splittingOfFunOnFintypeSurjective_injectiveₓ'. -/
theorem splittingOfFunOnFintypeSurjective_injective [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : Injective (splittingOfFunOnFintypeSurjective f s) :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/728baa2f54e6062c5879a3e397ac6bac323e506f
@@ -670,7 +670,7 @@ noncomputable def lift : (X → M) ≃+ ((X →₀ R) →ₗ[R] M) :=
lean 3 declaration is
forall (M : Type.{u1}) (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u3}) (f : LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (x : X), Eq.{succ u1} M (coeFn.{max (succ (max (max u3 u2) u1)) (succ 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(NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.instAdd.{u3, u1} X (fun (ᾰ : X) => M) (fun (i : X) => AddZeroClass.toHasAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (fun (_x : AddEquiv.{max (max u3 u2) u1, max u3 u1} (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R 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(NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))))))
but is expected to have type
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R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => X -> M) _x) (AddHomClass.toFunLike.{max (max u1 u3) u2, max (max u1 u3) u2, max u1 u2} (AddEquiv.{max (max u1 u3) u2, max u1 u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (LinearMap.instAddLinearMap.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.instAdd.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4991 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (AddZeroClass.toAdd.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddMonoid.toAddZeroClass.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (AddZeroClass.toAdd.{max u1 u2} (X -> M) (Pi.addZeroClass.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4991 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (AddMonoidHomClass.toAddHomClass.{max (max u1 u3) u2, max (max u1 u3) u2, max u1 u2} (AddEquiv.{max (max u1 u3) u2, max u1 u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (LinearMap.instAddLinearMap.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.instAdd.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4991 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (AddMonoid.toAddZeroClass.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Pi.addZeroClass.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4991 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddEquivClass.instAddMonoidHomClass.{max (max u1 u3) u2, max (max u1 u3) u2, max u1 u2} (AddEquiv.{max (max u1 u3) u2, max u1 u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (LinearMap.instAddLinearMap.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.instAdd.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4991 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (AddMonoid.toAddZeroClass.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Pi.addZeroClass.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4991 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddEquiv.instAddEquivClassAddEquiv.{max (max u1 u3) u2, max u1 u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (LinearMap.instAddLinearMap.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.instAdd.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4991 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))) (AddEquiv.symm.{max u1 u2, max (max u1 u3) u2} (X -> M) (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lift.{u1, u3, u2} M R _inst_1 _inst_3 _inst_4 X)) f x) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R 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+ forall (M : Type.{u1}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_3] (X : Type.{u2}) (f : LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (x : X), Eq.{succ u1} M (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2)} (AddEquiv.{max (max u1 u3) u2, 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u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (LinearMap.instAddLinearMap.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.instAdd.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5047 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (AddZeroClass.toAdd.{max (max u1 u3) u2} (LinearMap.{u3, 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (AddZeroClass.toAdd.{max u1 u2} (X -> M) (Pi.addZeroClass.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5047 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (AddMonoidHomClass.toAddHomClass.{max (max u1 u3) 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Case conversion may be inaccurate. Consider using '#align finsupp.lift_symm_apply Finsupp.lift_symm_applyₓ'. -/
@[simp]
theorem lift_symm_apply (f) (x) : ((lift M R X).symm f) x = f (single x 1) :=
@@ -681,13 +681,19 @@ theorem lift_symm_apply (f) (x) : ((lift M R X).symm f) x = f (single x 1) :=
lean 3 declaration is
forall (M : Type.{u1}) (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u3}) (f : X -> M) (g : Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))), Eq.{succ u1} M (coeFn.{max (succ (max u3 u2)) (succ u1), max (succ (max u3 u2)) (succ u1)} (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) 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AddZeroClass.toHasAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.hasAdd.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (fun (_x : AddEquiv.{max u3 u1, max (max u3 u2) u1} (X -> M) (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 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(NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) => (X -> M) -> (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R 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(Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (ᾰ : X) => M) (fun (i : X) => AddZeroClass.toHasAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.hasAdd.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.lift.{u1, u2, u3} M R _inst_1 _inst_3 _inst_4 X) f) g) (Finsupp.sum.{u3, u2, u1} X R M (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 g (fun (x : X) (r : R) => SMul.smul.{u2, u1} R M (SMulZeroClass.toHasSmul.{u2, u1} R M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u1} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4)))) r (f x)))
but is expected to have type
- forall (M : Type.{u1}) (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u3}) (f : X -> M) (g : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) g) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : X -> M) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) f) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (max (succ u1) (succ u2)) (succ u3)} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4991 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (fun (_x : X -> M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : X -> M) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) _x) (AddHomClass.toFunLike.{max (max u1 u2) u3, max u1 u3, max (max u1 u2) u3} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4991 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddZeroClass.toAdd.{max u1 u3} (X -> M) (Pi.addZeroClass.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4991 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (AddZeroClass.toAdd.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (AddMonoidHomClass.toAddHomClass.{max (max u1 u2) u3, max u1 u3, max (max u1 u2) u3} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4991 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.addZeroClass.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4991 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddEquivClass.instAddMonoidHomClass.{max (max u1 u2) u3, max u1 u3, max (max u1 u2) u3} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4991 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.addZeroClass.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4991 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddEquiv.instAddEquivClassAddEquiv.{max u1 u3, max (max u1 u2) u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4991 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (Finsupp.lift.{u1, u2, u3} M R _inst_1 _inst_3 _inst_4 X) f) g) (Finsupp.sum.{u3, u2, u1} X R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) _inst_3 g (fun (x : X) (r : R) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4))))) r (f x)))
+ forall (M : Type.{u1}) (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u3}) (f : X -> M) (g : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) g) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : X -> M) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) f) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (max (succ u1) (succ u2)) (succ u3)} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5047 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (fun (_x : X -> M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : X -> M) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) _x) (AddHomClass.toFunLike.{max (max u1 u2) u3, max u1 u3, max (max u1 u2) u3} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5047 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddZeroClass.toAdd.{max u1 u3} (X -> M) (Pi.addZeroClass.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5047 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (AddZeroClass.toAdd.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (AddMonoidHomClass.toAddHomClass.{max (max u1 u2) u3, max u1 u3, max (max u1 u2) u3} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5047 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.addZeroClass.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5047 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddEquivClass.instAddMonoidHomClass.{max (max u1 u2) u3, max u1 u3, max (max u1 u2) u3} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5047 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.addZeroClass.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5047 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddEquiv.instAddEquivClassAddEquiv.{max u1 u3, max (max u1 u2) u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5047 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (Finsupp.lift.{u1, u2, u3} M R _inst_1 _inst_3 _inst_4 X) f) g) (Finsupp.sum.{u3, u2, u1} X R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) _inst_3 g (fun (x : X) (r : R) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4))))) r (f x)))
Case conversion may be inaccurate. Consider using '#align finsupp.lift_apply Finsupp.lift_applyₓ'. -/
@[simp]
theorem lift_apply (f) (g) : ((lift M R X) f) g = g.Sum fun x r => r • f x :=
rfl
#align finsupp.lift_apply Finsupp.lift_apply
+/- warning: finsupp.llift -> Finsupp.llift is a dubious translation:
+lean 3 declaration is
+ forall (M : Type.{u1}) (R : Type.{u2}) (S : Type.{u3}) [_inst_1 : Semiring.{u2} R] [_inst_2 : Semiring.{u3} S] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u4}) [_inst_9 : Module.{u3, u1} S M _inst_2 _inst_3] [_inst_10 : SMulCommClass.{u2, u3, u1} R S M (SMulZeroClass.toHasSmul.{u2, u1} R M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u1} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u3, u1} S M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u1} S M (MulZeroClass.toHasZero.{u3} S (MulZeroOneClass.toMulZeroClass.{u3} S (MonoidWithZero.toMulZeroOneClass.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)))) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u1} S M (Semiring.toMonoidWithZero.{u3} S _inst_2) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Module.toMulActionWithZero.{u3, u1} S M _inst_2 _inst_3 _inst_9))))], LinearEquiv.{u3, u3, max u4 u1, max (max u4 u2) u1} S S _inst_2 _inst_2 (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2)) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2)) (RingHomInvPair.ids.{u3} S _inst_2) (RingHomInvPair.ids.{u3} S _inst_2) (X -> M) (LinearMap.{u2, u2, max u4 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u4, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u4, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.addCommMonoid.{u4, u1} X (fun (ᾰ : X) => M) (fun (i : X) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u4 u2, u1} R R (Finsupp.{u4, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.Function.module.{u4, u3, u1} X S M _inst_2 _inst_3 _inst_9) (LinearMap.module.{u2, u2, u3, max u4 u2, u1} R R S (Finsupp.{u4, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) _inst_2 _inst_9 _inst_10)
+but is expected to have type
+ forall (M : Type.{u1}) (R : Type.{u2}) (S : Type.{u3}) [_inst_1 : Semiring.{u2} R] [_inst_2 : Semiring.{u3} S] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u4}) [_inst_9 : Module.{u3, u1} S M _inst_2 _inst_3] [_inst_10 : SMulCommClass.{u2, u3, u1} R S M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u3, u1} S M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u1} S M (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u1} S M (Semiring.toMonoidWithZero.{u3} S _inst_2) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u3, u1} S M _inst_2 _inst_3 _inst_9))))], LinearEquiv.{u3, u3, max u1 u4, max u1 u2 u4} S S _inst_2 _inst_2 (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2)) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2)) (RingHomInvPair.ids.{u3} S _inst_2) (RingHomInvPair.ids.{u3} S _inst_2) (X -> M) (LinearMap.{u2, u2, max u2 u4, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u4, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.addCommMonoid.{u4, u1} X (fun (ᾰ : X) => M) (fun (i : X) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u2 u4, u1} R R (Finsupp.{u4, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u4, u1, u3} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u3, max u2 u4, u1} R R S (Finsupp.{u4, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) _inst_2 _inst_9 _inst_10)
+Case conversion may be inaccurate. Consider using '#align finsupp.llift Finsupp.lliftₓ'. -/
/-- Given compatible `S` and `R`-module structures on `M` and a type `X`, the set of functions
`X → M` is `S`-linearly equivalent to the `R`-linear maps from the free `R`-module
on `X` to `M`. -/
@@ -701,11 +707,23 @@ noncomputable def llift : (X → M) ≃ₗ[S] (X →₀ R) →ₗ[R] M :=
sum_single_index, zero_smul, one_smul, LinearMap.smul_apply] }
#align finsupp.llift Finsupp.llift
+/- warning: finsupp.llift_apply -> Finsupp.llift_apply is a dubious translation:
+lean 3 declaration is
+ forall (M : Type.{u1}) (R : Type.{u2}) (S : Type.{u3}) [_inst_1 : Semiring.{u2} R] [_inst_2 : Semiring.{u3} S] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u4}) [_inst_9 : Module.{u3, u1} S M _inst_2 _inst_3] [_inst_10 : SMulCommClass.{u2, u3, u1} R S M (SMulZeroClass.toHasSmul.{u2, u1} R M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u1} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u3, u1} S M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u1} S M (MulZeroClass.toHasZero.{u3} S (MulZeroOneClass.toMulZeroClass.{u3} S (MonoidWithZero.toMulZeroOneClass.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)))) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u1} S M (Semiring.toMonoidWithZero.{u3} S _inst_2) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Module.toMulActionWithZero.{u3, u1} S M _inst_2 _inst_3 _inst_9))))] (f : X -> M) (x : Finsupp.{u4, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))), Eq.{succ u1} M (coeFn.{max (succ (max u4 u2)) (succ u1), max (succ (max u4 u2)) (succ u1)} (LinearMap.{u2, u2, max u4 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u4, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u4, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u2, u2, max u4 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u4, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u4, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) => (Finsupp.{u4, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u2, u2, max u4 u2, u1} R R (Finsupp.{u4, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R 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+but is expected to have type
+ forall (M : Type.{u2}) (R : Type.{u3}) (S : Type.{u1}) [_inst_1 : Semiring.{u3} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (X : Type.{u4}) [_inst_9 : Module.{u1, u2} S M _inst_2 _inst_3] [_inst_10 : SMulCommClass.{u3, u1, u2} R S M (SMulZeroClass.toSMul.{u3, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u2} R M (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} S M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} S M (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u1, u2} S M _inst_2 _inst_3 _inst_9))))] (f : X -> M) (x : Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) => M) x) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : X -> M) => LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) f) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (fun (_x : Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u2) (succ u4), max (max (succ u2) (succ u3)) (succ u4)} (LinearEquiv.{u1, u1, max u2 u4, max u2 u3 u4} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R 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_inst_2)) (AddCommMonoid.toAddMonoid.{max u2 u4} (X -> M) (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3))) (Module.toDistribMulAction.{u1, max u2 u4} S (X -> M) _inst_2 (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (Pi.module.{u4, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9)))))) (SMulZeroClass.toSMul.{u1, max (max u2 u3) u4} S (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddMonoid.toZero.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u3) u4} S (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddMonoid.toAddZeroClass.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u3) u4} S (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u2 u3) u4} S (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) _inst_2 (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u3 u4, u2} R R S (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u3) u4, u1, max u2 u4, max (max u2 u3) u4} (LinearEquiv.{u1, u1, max u2 u4, max u2 u3 u4} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u4, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u3 u4, u2} R R S (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max u2 u4} (X -> M) (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Module.toDistribMulAction.{u1, max u2 u4} S (X -> M) _inst_2 (Pi.addCommMonoid.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (Pi.module.{u4, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9))) (Module.toDistribMulAction.{u1, max (max u2 u3) u4} S (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) _inst_2 (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u3 u4, u2} R R S (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max u2 u4, max (max u2 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_inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (X -> M) (fun (_x : X -> M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : X -> M) => LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) _x) (AddHomClass.toFunLike.{max (max u2 u3) u4, max u2 u4, max (max u2 u3) u4} (AddEquiv.{max u2 u4, max u2 u3 u4} (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (Pi.instAdd.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5047 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (LinearMap.instAddLinearMap.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddZeroClass.toAdd.{max u2 u4} (X -> M) (Pi.addZeroClass.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5047 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (AddZeroClass.toAdd.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddMonoid.toAddZeroClass.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (AddMonoidHomClass.toAddHomClass.{max (max u2 u3) u4, max u2 u4, max (max u2 u3) u4} (AddEquiv.{max u2 u4, max u2 u3 u4} (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (Pi.instAdd.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5047 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (LinearMap.instAddLinearMap.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (Pi.addZeroClass.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5047 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (AddMonoid.toAddZeroClass.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (AddEquivClass.instAddMonoidHomClass.{max (max u2 u3) u4, max u2 u4, max (max u2 u3) u4} (AddEquiv.{max u2 u4, max u2 u3 u4} (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (Pi.instAdd.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5047 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (LinearMap.instAddLinearMap.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (Pi.addZeroClass.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5047 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (AddMonoid.toAddZeroClass.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (AddEquiv.instAddEquivClassAddEquiv.{max u2 u4, max (max u2 u3) u4} (X -> M) (LinearMap.{u3, u3, max u3 u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (Pi.instAdd.{u4, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5047 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (LinearMap.instAddLinearMap.{u3, u3, max u3 u4, u2} R R (Finsupp.{u4, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) (Finsupp.lift.{u2, u3, u4} M R _inst_1 _inst_3 _inst_4 X) f) x)
+Case conversion may be inaccurate. Consider using '#align finsupp.llift_apply Finsupp.llift_applyₓ'. -/
@[simp]
theorem llift_apply (f : X → M) (x : X →₀ R) : llift M R S X f x = lift M R X f x :=
rfl
#align finsupp.llift_apply Finsupp.llift_apply
+/- warning: finsupp.llift_symm_apply -> Finsupp.llift_symm_apply is a dubious translation:
+lean 3 declaration is
+ forall (M : Type.{u1}) (R : Type.{u2}) (S : Type.{u3}) [_inst_1 : Semiring.{u2} R] [_inst_2 : Semiring.{u3} S] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u4}) [_inst_9 : Module.{u3, u1} S M _inst_2 _inst_3] [_inst_10 : SMulCommClass.{u2, u3, u1} R S M (SMulZeroClass.toHasSmul.{u2, u1} R M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u1} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u3, u1} S M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u1} S M (MulZeroClass.toHasZero.{u3} S (MulZeroOneClass.toMulZeroClass.{u3} S (MonoidWithZero.toMulZeroOneClass.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)))) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u1} S M (Semiring.toMonoidWithZero.{u3} S _inst_2) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Module.toMulActionWithZero.{u3, u1} S M _inst_2 _inst_3 _inst_9))))] (f : LinearMap.{u2, u2, max u4 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u4, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u4, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (x : X), Eq.{succ u1} M (coeFn.{max (succ (max (max u4 u2) u1)) (succ (max u4 u1)), max (succ (max (max u4 u2) u1)) (succ (max u4 u1))} (LinearEquiv.{u3, u3, max (max u4 u2) u1, max u4 u1} S S _inst_2 _inst_2 (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2)) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2)) (RingHomInvPair.ids.{u3} S _inst_2) (RingHomInvPair.ids.{u3} S _inst_2) (LinearMap.{u2, u2, max u4 u2, u1} R R _inst_1 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+but is expected to have type
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(Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} S M (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u1, u2} S M _inst_2 _inst_3 _inst_9))))] (f : LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (x 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_inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u1, max u4 u3, u2} R R S (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9))) S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (X -> M) (SMulZeroClass.toSMul.{u1, max (max u2 u4) u3} S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (AddMonoid.toZero.{max (max u2 u4) u3} (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u4) u3} S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (AddMonoid.toAddZeroClass.{max (max u2 u4) u3} (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u4) u3} S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) _inst_2 (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u1, max u4 u3, u2} R R S (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (SMulZeroClass.toSMul.{u1, max u2 u3} S (X -> M) (AddMonoid.toZero.{max u2 u3} (X -> M) (AddCommMonoid.toAddMonoid.{max u2 u3} (X -> M) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)))) (DistribSMul.toSMulZeroClass.{u1, max u2 u3} S (X -> M) (AddMonoid.toAddZeroClass.{max u2 u3} (X -> M) (AddCommMonoid.toAddMonoid.{max u2 u3} (X -> M) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)))) (DistribMulAction.toDistribSMul.{u1, max u2 u3} S (X -> M) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max u2 u3} (X -> M) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3))) (Module.toDistribMulAction.{u1, max u2 u3} S (X -> M) _inst_2 (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (Pi.module.{u3, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u4) u3, u1, max (max u2 u4) u3, max u2 u3} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u2 u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (X -> M) (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u1, max u4 u3, u2} R R S (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9))) S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (X -> M) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R 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(Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u3} (X -> M) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) _inst_2 (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u1, max u4 u3, u2} R R S (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (Module.toDistribMulAction.{u1, max u2 u3} S (X -> M) _inst_2 (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (Pi.module.{u3, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9))) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u2 u4) u3, max u2 u3, max (max u2 u4) u3} S (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4) (X -> M) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u2 u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u4, u4, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R 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(Pi.module.{u3, u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) S _inst_2 (fun (i : X) => _inst_3) (fun (i : X) => _inst_9))) _inst_2 (LinearMap.addCommMonoid.{u4, u4, max u4 u3, u2} R R (Finsupp.{u3, u4} X R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u4, u4} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_4 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.addCommMonoid.{u3, u2} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.5301 : X) => M) (fun (i : X) => _inst_3)) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u1, 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+Case conversion may be inaccurate. Consider using '#align finsupp.llift_symm_apply Finsupp.llift_symm_applyₓ'. -/
@[simp]
theorem llift_symm_apply (f : (X →₀ R) →ₗ[R] M) (x : X) :
(llift M R S X).symm f x = f (single x 1) :=
@@ -922,7 +940,7 @@ theorem total_single (c : R) (a : α) : Finsupp.total α M R v (single a c) = c
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (x : Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u1 u2} (α -> M) 0 (OfNat.mk.{max u1 u2} (α -> M) 0 (Zero.zero.{max u1 u2} (α -> M) (Pi.instZero.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))))))) x) (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))))))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u3 u1} (α -> M) 0 (Zero.toOfNat0.{max u3 u1} (α -> M) (Pi.instZero.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.6553 : α) => M) (fun (i : α) => AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) _inst_3))))
+ forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u3 u1} (α -> M) 0 (Zero.toOfNat0.{max u3 u1} (α -> M) (Pi.instZero.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.6886 : α) => M) (fun (i : α) => AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) _inst_3))))
Case conversion may be inaccurate. Consider using '#align finsupp.total_zero_apply Finsupp.total_zero_applyₓ'. -/
theorem total_zero_apply (x : α →₀ R) : (Finsupp.total α M R 0) x = 0 := by
simp [Finsupp.total_apply]
@@ -934,7 +952,7 @@ variable (α M)
lean 3 declaration is
forall (α : Type.{u1}) (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], Eq.{max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u1 u2} (α -> M) 0 (OfNat.mk.{max u1 u2} (α -> M) 0 (Zero.zero.{max u1 u2} (α -> M) (Pi.instZero.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))))))) (OfNat.ofNat.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) 0 (OfNat.mk.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) 0 (Zero.zero.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.hasZero.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))
but is expected to have type
- forall (α : Type.{u3}) (M : Type.{u2}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Eq.{max (max (succ u3) (succ u2)) (succ u1)} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u3 u2} (α -> M) 0 (Zero.toOfNat0.{max u3 u2} (α -> M) (Pi.instZero.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.6553 : α) => M) (fun (i : α) => AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))))) (OfNat.ofNat.{max (max u3 u2) u1} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) 0 (Zero.toOfNat0.{max (max u3 u2) u1} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (LinearMap.instZeroLinearMap.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))
+ forall (α : Type.{u3}) (M : Type.{u2}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Eq.{max (max (succ u3) (succ u2)) (succ u1)} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u3 u2} (α -> M) 0 (Zero.toOfNat0.{max u3 u2} (α -> M) (Pi.instZero.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.6886 : α) => M) (fun (i : α) => AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))))) (OfNat.ofNat.{max (max u3 u2) u1} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) 0 (Zero.toOfNat0.{max (max u3 u2) u1} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (LinearMap.instZeroLinearMap.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))
Case conversion may be inaccurate. Consider using '#align finsupp.total_zero Finsupp.total_zeroₓ'. -/
@[simp]
theorem total_zero : Finsupp.total α M R 0 = 0 :=
@@ -1773,7 +1791,7 @@ variable {S}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] {S : Type.{u4}} [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (f : α -> R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) => (α -> R) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (coeFn.{max (succ (max u1 u2)) (succ (max (max u1 u3) u2)), max (succ (max u1 u2)) (succ (max (max u1 u3) u2))} (LinearMap.{u4, u4, max u1 u2, max (max u1 u3) u2} S S _inst_5 _inst_5 (RingHom.id.{u4} S 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(Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) (fun (_x : LinearMap.{u4, u4, max u1 u2, max (max u1 u3) u2} S S _inst_5 _inst_5 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) => (α -> M) -> (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4)) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, max (max u1 u3) u2} S S (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) f) (Finset.sum.{u2, u1} M α _inst_3 (Finset.univ.{u1} α _inst_1) (fun (i : α) => SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (f i) (v i)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (f : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) f) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) v) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearMap.{u1, u1, max u3 u4, max u4 u3 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u3, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14128 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14128 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14128 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) f) (Finset.sum.{u4, u3} M α _inst_3 (Finset.univ.{u3} α _inst_1) (fun (i : α) => HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) (f i) (v i)))
+ forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M 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Case conversion may be inaccurate. Consider using '#align fintype.total_apply Fintype.total_applyₓ'. -/
theorem Fintype.total_apply (f) : Fintype.total R S v f = ∑ i, f i • v i :=
rfl
@@ -1783,7 +1801,7 @@ theorem Fintype.total_apply (f) : Fintype.total R S v f = ∑ i, f i • v i :=
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] {S : Type.{u4}} [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (i : α) (r : R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) => (α -> M) -> (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4)) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, max (max u1 u3) u2} S S (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) (Pi.single.{u1, u3} α (fun (ᾰ : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u1} α a b)) (fun (i : α) => MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) i r)) (SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) r (v i))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (i : α) (r : R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) (Pi.single.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) v) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearMap.{u1, u1, max u3 u4, max u4 u3 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R 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(i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14128 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14128 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) (Pi.single.{u3, u2} α (fun (ᾰ : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) r (v i))
+ forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (i : α) (r : R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) (Pi.single.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) v) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearMap.{u1, u1, max u3 u4, max u4 u3 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u3, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14461 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14461 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14461 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) (Pi.single.{u3, u2} α (fun (ᾰ : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) r (v i))
Case conversion may be inaccurate. Consider using '#align fintype.total_apply_single Fintype.total_apply_singleₓ'. -/
@[simp]
theorem Fintype.total_apply_single (i : α) (r : R) :
@@ -1799,7 +1817,7 @@ variable (S)
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] (S : Type.{u4}) [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (x : α -> R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))) M _inst_2 _inst_2 (Finsupp.addCommMonoid.{u1, 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(Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) x)
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (x : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) => M) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (α -> R) (fun (a : α -> R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> R) => Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) a) (SMulHomClass.toFunLike.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (α -> R) (AddMonoid.toZero.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (α -> R) (AddMonoid.toAddZeroClass.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (α -> R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u3 u2, max u3 u2, max u3 u2} R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) 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(a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (α -> R) (AddMonoid.toAddZeroClass.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (α -> R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u3 u2, max u3 u2, max u3 u2} R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u3 u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2)))))) (LinearEquiv.symm.{u2, u2, max u3 u2, max u3 u2} R R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (α -> R) _inst_2 _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (Finsupp.linearEquivFunOnFinite.{u2, u2, u3} R R α (Finite.of_fintype.{u3} α _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) _inst_2 (Semiring.toModule.{u2} R _inst_2))) x)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) v) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearMap.{u1, u1, max u3 u4, max u4 u3 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u3, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14128 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14128 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14128 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) x)
+ forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (x : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) => M) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (α -> R) (fun (a : α -> R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> R) => Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) a) (SMulHomClass.toFunLike.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (α -> R) (AddMonoid.toZero.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (α -> R) (AddMonoid.toAddZeroClass.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (α -> R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u3 u2, max u3 u2, max u3 u2} R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u3 u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2)))))) (LinearEquiv.symm.{u2, u2, max u3 u2, max u3 u2} R R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (α -> R) _inst_2 _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) _inst_2 (Semiring.toModule.{u2} R _inst_2))) x)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α 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_inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14461 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) x)
Case conversion may be inaccurate. Consider using '#align finsupp.total_eq_fintype_total_apply Finsupp.total_eq_fintype_total_applyₓ'. -/
theorem Finsupp.total_eq_fintype_total_apply (x : α → R) :
Finsupp.total α M R v ((Finsupp.linearEquivFunOnFinite R R α).symm x) = Fintype.total R S v x :=
@@ -1815,7 +1833,7 @@ theorem Finsupp.total_eq_fintype_total_apply (x : α → R) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] (S : Type.{u4}) [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (LinearMap.comp.{u3, u3, u3, max u1 u3, max u1 u3, u2} R R R (α -> R) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))) M _inst_2 _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHomCompTriple.right_ids.{u3, u3} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Finsupp.total.{u1, u2, u3} α M R _inst_2 _inst_3 _inst_4 v) (LinearEquiv.toLinearMap.{u3, u3, max u1 u3, max u1 u3} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHomInvPair.ids.{u3} R _inst_2) (RingHomInvPair.ids.{u3} R _inst_2) (α -> R) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))))) (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Pi.Function.module.{u1, 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(fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) => (α -> M) -> (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4)) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, max (max u1 u3) u2} S S (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)
but is expected to have type
- forall {α : Type.{u4}} {M : Type.{u3}} (R : Type.{u2}) [_inst_1 : Fintype.{u4} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u3} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u3} R S M (SMulZeroClass.toSMul.{u2, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u2, u3} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u3} S M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u1, u3} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (LinearMap.comp.{u2, u2, u2, max u4 u2, max u4 u2, u3} R R R (α -> R) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) M _inst_2 _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => 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(Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u4, max (max u2 u3) u4} S S (α -> M) (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u4, u3} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u4 u2, u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u4, u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14128 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u4 u2, u3} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u4, u3, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)
+ forall {α : Type.{u4}} {M : Type.{u3}} (R : Type.{u2}) [_inst_1 : Fintype.{u4} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u3} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u3} R S M (SMulZeroClass.toSMul.{u2, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u2, u3} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u3} S M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u1, u3} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (LinearMap.comp.{u2, u2, u2, max u4 u2, max u4 u2, u3} R R R (α -> R) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) M _inst_2 _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomCompTriple.ids.{u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Finsupp.total.{u4, u3, u2} α M R _inst_2 _inst_3 _inst_4 v) (LinearEquiv.toLinearMap.{u2, u2, max u4 u2, max u4 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u4, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (LinearEquiv.symm.{u2, u2, max u4 u2, max u4 u2} R R (Finsupp.{u4, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (α -> R) _inst_2 _inst_2 (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (Finsupp.linearEquivFunOnFinite.{u2, u2, u4} R R α (Finite.of_fintype.{u4} α _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) _inst_2 (Semiring.toModule.{u2} R _inst_2))))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), max (max (succ u2) (succ u3)) (succ u4)} (LinearMap.{u1, u1, max u4 u3, max u3 u4 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u4, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14461 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u4 u2, u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u4, u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14461 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u4 u2, u3} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u4, max (max u2 u3) u4} S S (α -> M) (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u4, u3} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u4 u2, u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u4, u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14461 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u4 u2, u3} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u4, u3, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)
Case conversion may be inaccurate. Consider using '#align finsupp.total_eq_fintype_total Finsupp.total_eq_fintype_totalₓ'. -/
theorem Finsupp.total_eq_fintype_total :
(Finsupp.total α M R v).comp (Finsupp.linearEquivFunOnFinite R R α).symm.toLinearMap =
@@ -1829,7 +1847,7 @@ variable {S}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] {S : Type.{u4}} [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{succ u2} (Submodule.{u3, u2} R M _inst_2 _inst_3 _inst_4) (LinearMap.range.{u3, u3, max u1 u3, u2, max (max u1 u3) u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (LinearMap.semilinearMapClass.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (RingHomSurjective.ids.{u3} R _inst_2) (coeFn.{max (succ (max u1 u2)) (succ (max (max u1 u3) u2)), max (succ (max u1 u2)) (succ (max (max u1 u3) u2))} (LinearMap.{u4, u4, max u1 u2, max (max u1 u3) u2} S S _inst_5 _inst_5 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) (fun (_x : LinearMap.{u4, u4, max u1 u2, max (max u1 u3) u2} S S _inst_5 _inst_5 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) => (α -> M) -> (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4)) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, max (max u1 u3) u2} S S (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)) (Submodule.span.{u3, u2} R M _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u1} M α v))
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u4}} (R : Type.{u3}) [_inst_1 : Fintype.{u2} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u3, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u1, u4} R S M (SMulZeroClass.toSMul.{u3, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u4} R M (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u4} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u3, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{succ u4} (Submodule.{u3, u4} R M _inst_2 _inst_3 _inst_4) (LinearMap.range.{u3, u3, max u2 u3, u4, max (max u2 u4) u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) v) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (RingHomSurjective.ids.{u3} R _inst_2) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearMap.{u1, u1, max u2 u4, max u4 u2 u3} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u2, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14128 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.module.{u2, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14128 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u2 u3, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u2, max (max u3 u4) u2} S S (α -> M) (LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u2, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.module.{u2, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14128 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u2 u3, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u2, u4, u3, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)) (Submodule.span.{u3, u4} R M _inst_2 _inst_3 _inst_4 (Set.range.{u4, succ u2} M α v))
+ forall {α : Type.{u2}} {M : Type.{u4}} (R : Type.{u3}) [_inst_1 : Fintype.{u2} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u3, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u1, u4} R S M (SMulZeroClass.toSMul.{u3, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u4} R M (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u4} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u3, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{succ u4} (Submodule.{u3, u4} R M _inst_2 _inst_3 _inst_4) (LinearMap.range.{u3, u3, max u2 u3, u4, max (max u2 u4) u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) v) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (RingHomSurjective.ids.{u3} R _inst_2) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearMap.{u1, u1, max u2 u4, max u4 u2 u3} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u2, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14461 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun 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NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u2, max (max u3 u4) u2} S S (α -> M) (LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u2, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.module.{u2, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14461 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u2 u3, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14473 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u2, u4, u3, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)) (Submodule.span.{u3, u4} R M _inst_2 _inst_3 _inst_4 (Set.range.{u4, succ u2} M α v))
Case conversion may be inaccurate. Consider using '#align fintype.range_total Fintype.range_totalₓ'. -/
@[simp]
theorem Fintype.range_total : (Fintype.total R S v).range = Submodule.span R (Set.range v) := by
@@ -2075,7 +2093,7 @@ theorem splittingOfFinsuppSurjective_injective (f : M →ₗ[R] α →₀ R) (s
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3)
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16729 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u1) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16729 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16729 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16729 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16729 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) _inst_3)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17062 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u1) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17062 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17062 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17062 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17062 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) _inst_3)
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective LinearMap.splittingOfFunOnFintypeSurjectiveₓ'. -/
-- See also `linear_map.splitting_of_finsupp_surjective`
/-- A surjective linear map to functions on a finite type has a splitting. -/
@@ -2089,7 +2107,7 @@ def splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R) (s
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Eq.{succ (max u3 u1)} (LinearMap.{u1, u1, max u3 u1, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (LinearMap.comp.{u1, u1, u1, max u3 u1, u2, max u3 u1} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomCompTriple.right_ids.{u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u1, max u3 u1} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16812 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16812 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16812 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16812 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Eq.{max (succ u2) (succ u3)} (LinearMap.{u2, u2, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16729 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16812 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.comp.{u2, u2, u2, max u2 u3, u1, max u2 u3} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16729 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16812 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u2, max u2 u3} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16729 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17145 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17145 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17145 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17145 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Eq.{max (succ u2) (succ u3)} (LinearMap.{u2, u2, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17062 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17145 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.comp.{u2, u2, u2, max u2 u3, u1, max u2 u3} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17062 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17145 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u2, max u2 u3} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17062 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)))
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective_splits LinearMap.splittingOfFunOnFintypeSurjective_splitsₓ'. -/
theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : f.comp (splittingOfFunOnFintypeSurjective f s) = LinearMap.id :=
@@ -2105,7 +2123,7 @@ theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R]
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Function.LeftInverse.{max (succ u3) (succ u1), succ u2} (α -> R) M (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f) (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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but is expected to have type
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16729 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16729 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => 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+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17277 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), 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Case conversion may be inaccurate. Consider using '#align linear_map.left_inverse_splitting_of_fun_on_fintype_surjective LinearMap.leftInverse_splittingOfFunOnFintypeSurjectiveₓ'. -/
theorem leftInverse_splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : LeftInverse f (splittingOfFunOnFintypeSurjective f s) := fun g =>
@@ -2116,7 +2134,7 @@ theorem leftInverse_splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Function.Injective.{max (succ u3) (succ u1), succ u2} (α -> R) M (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) (fun (_x : LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) => (α -> R) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, u2} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17003 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17003 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17003 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17003 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Function.Injective.{max (succ u2) (succ u3), succ u1} (α -> R) M (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16729 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16729 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16729 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17336 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17336 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17336 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17336 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Function.Injective.{max (succ u2) (succ u3), succ u1} (α -> R) M (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17062 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17062 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17062 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective_injective LinearMap.splittingOfFunOnFintypeSurjective_injectiveₓ'. -/
theorem splittingOfFunOnFintypeSurjective_injective [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : Injective (splittingOfFunOnFintypeSurjective f s) :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/728baa2f54e6062c5879a3e397ac6bac323e506f
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
! This file was ported from Lean 3 source module linear_algebra.finsupp
-! leanprover-community/mathlib commit 23aa88e32dcc9d2a24cca7bc23268567ed4cd7d6
+! leanprover-community/mathlib commit 3dec44d0b621a174c56e994da4aae15ba60110a2
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -650,7 +650,7 @@ end Lsum
section
-variable (M) (R) (X : Type _)
+variable (M) (R) (X : Type _) (S) [Module S M] [SMulCommClass R S M]
/- warning: finsupp.lift -> Finsupp.lift is a dubious translation:
lean 3 declaration is
@@ -688,6 +688,30 @@ theorem lift_apply (f) (g) : ((lift M R X) f) g = g.Sum fun x r => r • f x :=
rfl
#align finsupp.lift_apply Finsupp.lift_apply
+/-- Given compatible `S` and `R`-module structures on `M` and a type `X`, the set of functions
+`X → M` is `S`-linearly equivalent to the `R`-linear maps from the free `R`-module
+on `X` to `M`. -/
+noncomputable def llift : (X → M) ≃ₗ[S] (X →₀ R) →ₗ[R] M :=
+ { lift M R X with
+ map_smul' := by
+ intros
+ dsimp
+ ext
+ simp only [coe_comp, Function.comp_apply, lsingle_apply, lift_apply, Pi.smul_apply,
+ sum_single_index, zero_smul, one_smul, LinearMap.smul_apply] }
+#align finsupp.llift Finsupp.llift
+
+@[simp]
+theorem llift_apply (f : X → M) (x : X →₀ R) : llift M R S X f x = lift M R X f x :=
+ rfl
+#align finsupp.llift_apply Finsupp.llift_apply
+
+@[simp]
+theorem llift_symm_apply (f : (X →₀ R) →ₗ[R] M) (x : X) :
+ (llift M R S X).symm f x = f (single x 1) :=
+ rfl
+#align finsupp.llift_symm_apply Finsupp.llift_symm_apply
+
end
section LmapDomain
mathlib commit https://github.com/leanprover-community/mathlib/commit/57e09a1296bfb4330ddf6624f1028ba186117d82
@@ -2051,7 +2051,7 @@ theorem splittingOfFinsuppSurjective_injective (f : M →ₗ[R] α →₀ R) (s
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3)
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16729 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u1) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16729 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16729 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16729 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16744 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) _inst_3)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16729 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u1) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16729 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16729 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16729 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16729 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) _inst_3)
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective LinearMap.splittingOfFunOnFintypeSurjectiveₓ'. -/
-- See also `linear_map.splitting_of_finsupp_surjective`
/-- A surjective linear map to functions on a finite type has a splitting. -/
@@ -2065,7 +2065,7 @@ def splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R) (s
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Eq.{succ (max u3 u1)} (LinearMap.{u1, u1, max u3 u1, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (LinearMap.comp.{u1, u1, u1, max u3 u1, u2, max u3 u1} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomCompTriple.right_ids.{u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u1, max u3 u1} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16812 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16812 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16812 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16812 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Eq.{max (succ u2) (succ u3)} (LinearMap.{u2, u2, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16744 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16812 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.comp.{u2, u2, u2, max u2 u3, u1, max u2 u3} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16744 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16812 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u2, max u2 u3} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16744 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16812 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16812 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16812 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16812 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Eq.{max (succ u2) (succ u3)} (LinearMap.{u2, u2, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16729 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16812 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.comp.{u2, u2, u2, max u2 u3, u1, max u2 u3} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16729 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16812 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u2, max u2 u3} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16729 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)))
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective_splits LinearMap.splittingOfFunOnFintypeSurjective_splitsₓ'. -/
theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : f.comp (splittingOfFunOnFintypeSurjective f s) = LinearMap.id :=
@@ -2081,7 +2081,7 @@ theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R]
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Function.LeftInverse.{max (succ u3) (succ u1), succ u2} (α -> R) M (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f) (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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but is expected to have type
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16744 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16744 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => 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+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16944 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), 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Case conversion may be inaccurate. Consider using '#align linear_map.left_inverse_splitting_of_fun_on_fintype_surjective LinearMap.leftInverse_splittingOfFunOnFintypeSurjectiveₓ'. -/
theorem leftInverse_splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : LeftInverse f (splittingOfFunOnFintypeSurjective f s) := fun g =>
@@ -2092,7 +2092,7 @@ theorem leftInverse_splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Function.Injective.{max (succ u3) (succ u1), succ u2} (α -> R) M (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) (fun (_x : LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) => (α -> R) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, u2} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17003 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17003 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17003 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17003 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Function.Injective.{max (succ u2) (succ u3), succ u1} (α -> R) M (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16744 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16744 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16744 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17003 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17003 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17003 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17003 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Function.Injective.{max (succ u2) (succ u3), succ u1} (α -> R) M (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16729 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16729 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16729 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective_injective LinearMap.splittingOfFunOnFintypeSurjective_injectiveₓ'. -/
theorem splittingOfFunOnFintypeSurjective_injective [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : Injective (splittingOfFunOnFintypeSurjective f s) :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/02ba8949f486ebecf93fe7460f1ed0564b5e442c
@@ -255,7 +255,7 @@ theorem supᵢ_lsingle_range : (⨆ a, (lsingle a : M →ₗ[R] α →₀ M).ran
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α) (t : Set.{u1} α), (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) s t) -> (Disjoint.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) (Submodule.orderBot.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (supᵢ.{max u1 u2, succ u1} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => supᵢ.{max u1 u2, 0} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LinearMap.range.{u3, u3, u2, max u1 u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u3, u3, u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R _inst_1) (Finsupp.lsingle.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a)))) (supᵢ.{max u1 u2, succ u1} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => supᵢ.{max u1 u2, 0} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a t) => LinearMap.range.{u3, u3, u2, max u1 u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u3, u3, u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R _inst_1) (Finsupp.lsingle.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a)))))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (t : Set.{u3} α), (Disjoint.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} α) (Preorder.toLE.{u3} (Set.{u3} α) (PartialOrder.toPreorder.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) s t) -> (Disjoint.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (supᵢ.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => supᵢ.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) (fun (H : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a)))) (supᵢ.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => supᵢ.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a t) (fun (H : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a t) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a)))))
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (t : Set.{u3} α), (Disjoint.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} α) (Preorder.toLE.{u3} (Set.{u3} α) (PartialOrder.toPreorder.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) s t) -> (Disjoint.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (supᵢ.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => supᵢ.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) (fun (H : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a)))) (supᵢ.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => supᵢ.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a t) (fun (H : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a t) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a)))))
Case conversion may be inaccurate. Consider using '#align finsupp.disjoint_lsingle_lsingle Finsupp.disjoint_lsingle_lsingleₓ'. -/
theorem disjoint_lsingle_lsingle (s t : Set α) (hs : Disjoint s t) :
Disjoint (⨆ a ∈ s, (lsingle a : M →ₗ[R] α →₀ M).range)
@@ -314,7 +314,7 @@ variable {M}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {s : Set.{u1} α} (p : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))), Iff (Membership.Mem.{max u1 u2, max u1 u2} (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) p (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} α) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (Finset.Set.hasCoeT.{u1} α))) (Finsupp.support.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) p)) s)
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {s : Set.{u3} α} (p : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))), Iff (Membership.mem.{max u3 u2, max u2 u3} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) p (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (HasSubset.Subset.{u3} (Set.{u3} α) (Set.instHasSubsetSet.{u3} α) (Finset.toSet.{u3} α (Finsupp.support.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) p)) s)
+ forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {s : Set.{u3} α} (p : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))), Iff (Membership.mem.{max u3 u2, max u2 u3} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.setLike.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) p (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (HasSubset.Subset.{u3} (Set.{u3} α) (Set.instHasSubsetSet.{u3} α) (Finset.toSet.{u3} α (Finsupp.support.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) p)) s)
Case conversion may be inaccurate. Consider using '#align finsupp.mem_supported Finsupp.mem_supportedₓ'. -/
theorem mem_supported {s : Set α} (p : α →₀ M) : p ∈ supported M R s ↔ ↑p.support ⊆ s :=
Iff.rfl
@@ -324,7 +324,7 @@ theorem mem_supported {s : Set α} (p : α →₀ M) : p ∈ supported M R s ↔
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {s : Set.{u1} α} (p : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))), Iff (Membership.Mem.{max u1 u2, max u1 u2} (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) p (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (forall (x : α), (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s)) -> (Eq.{succ u2} M (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (fun (_x : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) => α -> M) (Finsupp.coeFun.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) p x) (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))))))))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {s : Set.{u3} α} (p : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))), Iff (Membership.mem.{max u3 u2, max u2 u3} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) p (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (forall (x : α), (Not (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) x s)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) x) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) α (fun (_x : α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) _x) (Finsupp.funLike.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) p x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) x) (AddMonoid.toZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) x) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) x) _inst_3))))))
+ forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {s : Set.{u3} α} (p : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))), Iff (Membership.mem.{max u3 u2, max u2 u3} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.setLike.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) p (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (forall (x : α), (Not (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) x s)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) x) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) α (fun (_x : α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) _x) (Finsupp.funLike.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) p x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) x) (AddMonoid.toZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) x) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) x) _inst_3))))))
Case conversion may be inaccurate. Consider using '#align finsupp.mem_supported' Finsupp.mem_supported'ₓ'. -/
/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ∉ » s) -/
theorem mem_supported' {s : Set α} (p : α →₀ M) :
@@ -337,7 +337,7 @@ theorem mem_supported' {s : Set α} (p : α →₀ M) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (p : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))), Membership.Mem.{max u1 u2, max u1 u2} (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) p (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} α) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (Finset.Set.hasCoeT.{u1} α))) (Finsupp.support.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) p)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (p : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))), Membership.mem.{max u3 u2, max u2 u3} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) p (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (Finset.toSet.{u3} α (Finsupp.support.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) p)))
+ forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (p : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))), Membership.mem.{max u3 u2, max u2 u3} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.setLike.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) p (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (Finset.toSet.{u3} α (Finsupp.support.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) p)))
Case conversion may be inaccurate. Consider using '#align finsupp.mem_supported_support Finsupp.mem_supported_supportₓ'. -/
theorem mem_supported_support (p : α →₀ M) : p ∈ Finsupp.supported M R (p.support : Set α) := by
rw [Finsupp.mem_supported]
@@ -347,7 +347,7 @@ theorem mem_supported_support (p : α →₀ M) : p ∈ Finsupp.supported M R (p
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {s : Set.{u1} α} {a : α} (b : M), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (Membership.Mem.{max u1 u2, max u1 u2} (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) (Finsupp.single.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) a b) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {s : Set.{u3} α} {a : α} (b : M), (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) -> (Membership.mem.{max u2 u3, max u2 u3} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) (Finsupp.single.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) a b) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s))
+ forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {s : Set.{u3} α} {a : α} (b : M), (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) -> (Membership.mem.{max u2 u3, max u2 u3} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.setLike.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) (Finsupp.single.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) a b) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s))
Case conversion may be inaccurate. Consider using '#align finsupp.single_mem_supported Finsupp.single_mem_supportedₓ'. -/
theorem single_mem_supported {s : Set α} {a : α} (b : M) (h : a ∈ s) :
single a b ∈ supported M R s :=
@@ -380,7 +380,7 @@ variable (M R)
lean 3 declaration is
forall {α : Type.{u1}} (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α), LinearMap.{u3, u3, max u1 u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Submodule.addCommMonoid.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Submodule.module.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s))
but is expected to have type
- forall {α : Type.{u1}} (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α), LinearMap.{u3, u3, max u2 u1, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Subtype.{succ (max u1 u2)} (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u1 u2, max u1 u2} (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u3, max u2 u1} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u3, max u2 u1} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) x (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s))
+ forall {α : Type.{u1}} (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α), LinearMap.{u3, u3, max u2 u1, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Subtype.{succ (max u1 u2)} (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u1 u2, max u1 u2} (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u3, max u2 u1} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u3, max u2 u1} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) x (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Submodule.addCommMonoid.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Submodule.module.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s))
Case conversion may be inaccurate. Consider using '#align finsupp.restrict_dom Finsupp.restrictDomₓ'. -/
/-- Interpret `finsupp.filter s` as a linear map from `α →₀ M` to `supported M R s`. -/
def restrictDom (s : Set α) : (α →₀ M) →ₗ[R] supported M R s :=
@@ -399,7 +399,7 @@ section
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α) (l : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))), Eq.{max (succ u1) (succ u2)} (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) ((fun (a : Type.{max u1 u2}) (b : Sort.{max (succ u1) (succ u2)}) [self : HasLiftT.{succ (max u1 u2), max (succ u1) (succ u2)} a b] => self.0) (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, 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but is expected to have type
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(Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Submodule.addCommMonoid.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Submodule.module.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.restrictDom.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) l)) (Finsupp.filter.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (fun (_x : α) => Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) _x s) l)
Case conversion may be inaccurate. Consider using '#align finsupp.restrict_dom_apply Finsupp.restrictDom_applyₓ'. -/
@[simp]
theorem restrictDom_apply (s : Set α) (l : α →₀ M) :
@@ -413,7 +413,7 @@ end
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α), Eq.{succ (max u1 u2)} (LinearMap.{u3, u3, max u1 u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M 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(Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s))) (LinearMap.comp.{u3, u3, u3, max u1 u2, max u1 u2, max u1 u2} R R R (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) _inst_1 _inst_1 _inst_1 (Submodule.addCommMonoid.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.addCommMonoid.{u1, u2} α 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(Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomCompTriple.right_ids.{u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.restrictDom.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s) (Submodule.subtype.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s))) (LinearMap.id.{u3, max u1 u2} R (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M 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but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α), Eq.{max (succ u3) (succ u2)} (LinearMap.{u1, u1, max u3 u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Subtype.{succ (max u3 u2)} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u3 u2, max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u3 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max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) x (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) 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(AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) x (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s))) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Subtype.{succ (max u3 u2)} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u3 u2, max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) x (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s))) _inst_1 _inst_1 _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) 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(AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u3 u2, max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) x (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s))) _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)))
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α), Eq.{max (succ u3) (succ u2)} (LinearMap.{u1, u1, max u3 u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Subtype.{succ (max u3 u2)} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u3 u2, max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u3 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Case conversion may be inaccurate. Consider using '#align finsupp.restrict_dom_comp_subtype Finsupp.restrictDom_comp_subtypeₓ'. -/
theorem restrictDom_comp_subtype (s : Set α) :
(restrictDom M R s).comp (Submodule.subtype _) = LinearMap.id :=
@@ -427,7 +427,7 @@ theorem restrictDom_comp_subtype (s : Set α) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α), Eq.{succ (max u1 u2)} (Submodule.{u3, max u1 u2} R (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M 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but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α), Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u3 u2} R (Subtype.{succ (max u3 u2)} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u3 u2, max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) 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+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α), Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u3 u2} R (Subtype.{succ (max u3 u2)} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u3 u2, max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) 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_inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.setLike.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) x (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s))) (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Submodule.addCommMonoid.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Submodule.module.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u3 u2, max u3 u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Subtype.{succ (max u3 u2)} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u3 u2, max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.setLike.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) x (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Submodule.addCommMonoid.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Submodule.module.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.restrictDom.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (Top.top.{max u3 u2} (Submodule.{u1, max u3 u2} R (Subtype.{succ (max u3 u2)} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u3 u2, max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.setLike.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) x (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s))) _inst_1 (Submodule.addCommMonoid.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (Submodule.module.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s))) (Submodule.instTopSubmodule.{u1, max u3 u2} R (Subtype.{succ (max u3 u2)} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u3 u2, max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.setLike.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) x (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s))) _inst_1 (Submodule.addCommMonoid.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (Submodule.module.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s))))
Case conversion may be inaccurate. Consider using '#align finsupp.range_restrict_dom Finsupp.range_restrictDomₓ'. -/
theorem range_restrictDom (s : Set α) : (restrictDom M R s).range = ⊤ :=
range_eq_top.2 <|
@@ -525,7 +525,7 @@ theorem supported_inter (s t : Set α) : supported M R (s ∩ t) = supported M R
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {s : Set.{u1} α} {t : Set.{u1} α}, (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) s t) -> (Disjoint.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) (Submodule.orderBot.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 t))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {s : Set.{u3} α} {t : Set.{u3} α}, (Disjoint.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} α) (Preorder.toLE.{u3} (Set.{u3} α) (PartialOrder.toPreorder.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) s t) -> (Disjoint.{max u2 u3} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 t))
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {s : Set.{u3} α} {t : Set.{u3} α}, (Disjoint.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} α) (Preorder.toLE.{u3} (Set.{u3} α) (PartialOrder.toPreorder.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) s t) -> (Disjoint.{max u2 u3} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 t))
Case conversion may be inaccurate. Consider using '#align finsupp.disjoint_supported_supported Finsupp.disjoint_supported_supportedₓ'. -/
theorem disjoint_supported_supported {s t : Set α} (h : Disjoint s t) :
Disjoint (supported M R s) (supported M R t) :=
@@ -536,7 +536,7 @@ theorem disjoint_supported_supported {s t : Set α} (h : Disjoint s t) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] [_inst_9 : Nontrivial.{u2} M] {s : Set.{u1} α} {t : Set.{u1} α}, Iff (Disjoint.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) (Submodule.orderBot.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 t)) (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) s t)
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u3}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u1, u3} R M _inst_1 _inst_3] [_inst_9 : Nontrivial.{u3} M] {s : Set.{u2} α} {t : Set.{u2} α}, Iff (Disjoint.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) (Finsupp.module.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) (Finsupp.module.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) (Finsupp.module.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u2 u3} R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) (Finsupp.module.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4)))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u1, max u2 u3} R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) (Finsupp.module.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4 s) (Finsupp.supported.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4 t)) (Disjoint.{u2} (Set.{u2} α) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} α) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α)))))) (BoundedOrder.toOrderBot.{u2} (Set.{u2} α) (Preorder.toLE.{u2} (Set.{u2} α) (PartialOrder.toPreorder.{u2} (Set.{u2} α) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} α) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α)))))))) (CompleteLattice.toBoundedOrder.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α)))))) s t)
+ forall {α : Type.{u2}} {M : Type.{u3}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u1, u3} R M _inst_1 _inst_3] [_inst_9 : Nontrivial.{u3} M] {s : Set.{u2} α} {t : Set.{u2} α}, Iff (Disjoint.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) (Finsupp.module.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) (Finsupp.module.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) (Finsupp.module.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u2 u3} R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) (Finsupp.module.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4)))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u1, max u2 u3} R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) (Finsupp.module.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4 s) (Finsupp.supported.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4 t)) (Disjoint.{u2} (Set.{u2} α) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} α) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α)))))) (BoundedOrder.toOrderBot.{u2} (Set.{u2} α) (Preorder.toLE.{u2} (Set.{u2} α) (PartialOrder.toPreorder.{u2} (Set.{u2} α) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} α) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α)))))))) (CompleteLattice.toBoundedOrder.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α)))))) s t)
Case conversion may be inaccurate. Consider using '#align finsupp.disjoint_supported_supported_iff Finsupp.disjoint_supported_supported_iffₓ'. -/
theorem disjoint_supported_supported_iff [Nontrivial M] {s t : Set α} :
Disjoint (supported M R s) (supported M R t) ↔ Disjoint s t :=
@@ -552,7 +552,7 @@ theorem disjoint_supported_supported_iff [Nontrivial M] {s t : Set α} :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α), LinearEquiv.{u3, u3, max u1 u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.addCommMonoid.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.addCommMonoid.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) M _inst_3) (Submodule.module.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.module.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) M R _inst_1 _inst_3 _inst_4)
but is expected to have type
- forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α), LinearEquiv.{u3, u3, max u1 u2, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Subtype.{succ (max u1 u2)} (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u1 u2, max u1 u2} (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u3, max u2 u1} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u3, max u2 u1} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) x (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s))) (Finsupp.{u1, u2} (Set.Elem.{u1} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.addCommMonoid.{u1, u2} (Set.Elem.{u1} α s) M _inst_3) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.module.{u1, u2, u3} (Set.Elem.{u1} α s) M R _inst_1 _inst_3 _inst_4)
+ forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α), LinearEquiv.{u3, u3, max u1 u2, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Subtype.{succ (max u1 u2)} (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u1 u2, max u1 u2} (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u3, max u2 u1} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u3, max u2 u1} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) x (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s))) (Finsupp.{u1, u2} (Set.Elem.{u1} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.addCommMonoid.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.addCommMonoid.{u1, u2} (Set.Elem.{u1} α s) M _inst_3) (Submodule.module.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.module.{u1, u2, u3} (Set.Elem.{u1} α s) M R _inst_1 _inst_3 _inst_4)
Case conversion may be inaccurate. Consider using '#align finsupp.supported_equiv_finsupp Finsupp.supportedEquivFinsuppₓ'. -/
/-- Interpret `finsupp.restrict_support_equiv` as a linear equivalence between
`supported M R s` and `s →₀ M`. -/
@@ -786,7 +786,7 @@ theorem lmapDomain_supported [Nonempty α] (f : α → α') (s : Set α) :
lean 3 declaration is
forall {α : Type.{u1}} (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {α' : Type.{u4}} (f : α -> α') {s : Set.{u1} α}, (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (Eq.{succ u4} α' (f a) (f b)) -> (Eq.{succ u1} α a b))) -> (Disjoint.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) (Submodule.orderBot.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s) (LinearMap.ker.{u3, u3, max u1 u2, max u4 u2, max (max u1 u2) u4 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, max u1 u2, max u4 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u3, u3, max u1 u2, max u4 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lmapDomain.{u1, u2, u3, u4} α M R _inst_1 _inst_3 _inst_4 α' f)))
but is expected to have type
- forall {α : Type.{u4}} (M : Type.{u2}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {α' : Type.{u3}} (f : α -> α') {s : Set.{u4} α}, (forall (a : α), (Membership.mem.{u4, u4} α (Set.{u4} α) (Set.instMembershipSet.{u4} α) a s) -> (forall (b : α), (Membership.mem.{u4, u4} α (Set.{u4} α) (Set.instMembershipSet.{u4} α) b s) -> (Eq.{succ u3} α' (f a) (f b)) -> (Eq.{succ u4} α a b))) -> (Disjoint.{max u2 u4} (Submodule.{u1, max u2 u4} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u4 u2} (Submodule.{u1, max u2 u4} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u4 u2} (Submodule.{u1, max u2 u4} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u4 u2} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u1, max u4 u2} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) (LinearMap.ker.{u1, u1, max u4 u2, max u2 u3, max (max u2 u3) u4} R R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u4, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α' M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u4 u2, max u2 u3} R R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lmapDomain.{u4, u2, u1, u3} α M R _inst_1 _inst_3 _inst_4 α' f)))
+ forall {α : Type.{u4}} (M : Type.{u2}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {α' : Type.{u3}} (f : α -> α') {s : Set.{u4} α}, (forall (a : α), (Membership.mem.{u4, u4} α (Set.{u4} α) (Set.instMembershipSet.{u4} α) a s) -> (forall (b : α), (Membership.mem.{u4, u4} α (Set.{u4} α) (Set.instMembershipSet.{u4} α) b s) -> (Eq.{succ u3} α' (f a) (f b)) -> (Eq.{succ u4} α a b))) -> (Disjoint.{max u2 u4} (Submodule.{u1, max u2 u4} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u4 u2} (Submodule.{u1, max u2 u4} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u4 u2} (Submodule.{u1, max u2 u4} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u4 u2} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u1, max u4 u2} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) (LinearMap.ker.{u1, u1, max u4 u2, max u2 u3, max (max u2 u3) u4} R R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u4, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α' M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u4 u2, max u2 u3} R R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lmapDomain.{u4, u2, u1, u3} α M R _inst_1 _inst_3 _inst_4 α' f)))
Case conversion may be inaccurate. Consider using '#align finsupp.lmap_domain_disjoint_ker Finsupp.lmapDomain_disjoint_kerₓ'. -/
/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a b «expr ∈ » s) -/
theorem lmapDomain_disjoint_ker (f : α → α') {s : Set α}
@@ -875,7 +875,7 @@ theorem total_apply (l : α →₀ R) : Finsupp.total α M R v l = l.Sum fun i a
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {v : α -> M} {l : Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))} {s : Finset.{u1} α}, (Membership.Mem.{max u1 u3, max u1 u3} (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (SetLike.hasMem.{max u1 u3, max u1 u3} (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) (Submodule.setLike.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)))) l (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} α) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (Finset.Set.hasCoeT.{u1} α))) s))) -> (Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v) l) (Finset.sum.{u2, u1} M α _inst_3 s (fun (i : α) => SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (fun (_x : Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) => α -> R) (Finsupp.coeFun.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) l i) (v i))))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {v : α -> M} {l : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))} {s : Finset.{u3} α}, (Membership.mem.{max u3 u2, max u2 u3} (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 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R _inst_1))) (Semiring.toModule.{u2} R _inst_1) (Finset.toSet.{u3} α s))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 v) l) (Finset.sum.{u1, u3} M α _inst_3 s (fun (i : α) => HSMul.hSMul.{u2, u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M M (instHSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (SMulZeroClass.toSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M _inst_1 _inst_3 _inst_4))))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) α (fun (_x : α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) _x) (Finsupp.funLike.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) l i) (v i))))
+ forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {v : α -> M} {l : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))} {s : Finset.{u3} α}, (Membership.mem.{max u3 u2, max u2 u3} (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 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(Semiring.toModule.{u2} R _inst_1) (Finset.toSet.{u3} α s))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 v) l) (Finset.sum.{u1, u3} M α _inst_3 s (fun (i : α) => HSMul.hSMul.{u2, u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M M (instHSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (SMulZeroClass.toSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M _inst_1 _inst_3 _inst_4))))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) α (fun (_x : α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) _x) (Finsupp.funLike.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) l i) (v i))))
Case conversion may be inaccurate. Consider using '#align finsupp.total_apply_of_mem_supported Finsupp.total_apply_of_mem_supportedₓ'. -/
theorem total_apply_of_mem_supported {l : α →₀ R} {s : Finset α}
(hs : l ∈ supported R R (↑s : Set α)) : Finsupp.total α M R v l = s.Sum fun i => l i • v i :=
@@ -1076,7 +1076,7 @@ theorem span_eq_range_total (s : Set M) : span R s = (Finsupp.total s M R coe).r
lean 3 declaration is
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but is expected to have type
- forall {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u2} M) (x : M), Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 s)) (Exists.{max (succ u2) (succ u1)} (Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (l : Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} (Set.Elem.{u2} M s) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u1, u1} (Set.Elem.{u2} M s) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u2} R R (Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} (Set.Elem.{u2} M s) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u1, u1} (Set.Elem.{u2} M s) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} (Set.Elem.{u2} M s) M R _inst_1 _inst_3 _inst_4 (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s))) l) x))
+ forall {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u2} M) (x : M), Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 s)) (Exists.{max (succ u2) (succ u1)} (Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (l : Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} (Set.Elem.{u2} M s) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u1, u1} (Set.Elem.{u2} M s) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u2} R R (Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} (Set.Elem.{u2} M s) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u1, u1} (Set.Elem.{u2} M s) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} (Set.Elem.{u2} M s) M R _inst_1 _inst_3 _inst_4 (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s))) l) x))
Case conversion may be inaccurate. Consider using '#align finsupp.mem_span_iff_total Finsupp.mem_span_iff_totalₓ'. -/
theorem mem_span_iff_total (s : Set M) (x : M) :
x ∈ span R s ↔ ∃ l : s →₀ R, Finsupp.total s M R coe l = x :=
@@ -1089,7 +1089,7 @@ variable {R}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {v : α -> M} {x : M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u3, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.range.{u2, succ u1} M α v))) (Exists.{max (succ u1) (succ u3)} (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (fun (c : Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) => Eq.{succ u2} M (Finsupp.sum.{u1, u3, u2} α R M (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 c (fun (i : α) (a : R) => SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) a (v i))) x))
but is expected to have type
- forall {α : Type.{u1}} {M : Type.{u3}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_1 _inst_3] {v : α -> M} {x : M}, Iff (Membership.mem.{u3, u3} M (Submodule.{u2, u3} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u3} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u2, u3} R M _inst_1 _inst_3 _inst_4 (Set.range.{u3, succ u1} M α v))) (Exists.{max (succ u1) (succ u2)} (Finsupp.{u1, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (c : Finsupp.{u1, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => Eq.{succ u3} M (Finsupp.sum.{u1, u2, u3} α R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) _inst_3 c (fun (i : α) (a : R) => HSMul.hSMul.{u2, u3, u3} R M M (instHSMul.{u2, u3} R M (SMulZeroClass.toSMul.{u2, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u2, u3} R M _inst_1 _inst_3 _inst_4))))) a (v i))) x))
+ forall {α : Type.{u1}} {M : Type.{u3}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_1 _inst_3] {v : α -> M} {x : M}, Iff (Membership.mem.{u3, u3} M (Submodule.{u2, u3} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u3} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u2, u3} R M _inst_1 _inst_3 _inst_4 (Set.range.{u3, succ u1} M α v))) (Exists.{max (succ u1) (succ u2)} (Finsupp.{u1, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (c : Finsupp.{u1, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => Eq.{succ u3} M (Finsupp.sum.{u1, u2, u3} α R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) _inst_3 c (fun (i : α) (a : R) => HSMul.hSMul.{u2, u3, u3} R M M (instHSMul.{u2, u3} R M (SMulZeroClass.toSMul.{u2, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u2, u3} R M _inst_1 _inst_3 _inst_4))))) a (v i))) x))
Case conversion may be inaccurate. Consider using '#align finsupp.mem_span_range_iff_exists_finsupp Finsupp.mem_span_range_iff_exists_finsuppₓ'. -/
theorem mem_span_range_iff_exists_finsupp {v : α → M} {x : M} :
x ∈ span R (range v) ↔ ∃ c : α →₀ R, (c.Sum fun i a => a • v i) = x := by
@@ -1128,7 +1128,7 @@ theorem span_image_eq_map_total (s : Set α) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {v : α -> M} {s : Set.{u1} α} {x : M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u3, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s))) (Exists.{succ (max u1 u3)} (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (fun (l : Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) => Exists.{0} (Membership.Mem.{max u1 u3, max u1 u3} (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (SetLike.hasMem.{max u1 u3, max u1 u3} (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) (Submodule.setLike.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)))) l (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s)) (fun (H : Membership.Mem.{max u1 u3, max u1 u3} (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (SetLike.hasMem.{max u1 u3, max u1 u3} (Submodule.{u3, max u1 u3} R 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(NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v) l) x)))
but is expected to have type
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(Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) => And (Membership.mem.{max u3 u1, max u1 u3} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) 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_inst_1)))))) (Submodule.instSetLikeSubmodule.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) l (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u1), succ u2} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (a : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) a) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 v) l) x)))
+ forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {v : α -> M} {s : Set.{u3} α} {x : M}, Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (Exists.{succ (max u3 u1)} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (fun (l : Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) => And (Membership.mem.{max u3 u1, max u1 u3} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{max u3 u1, max u3 u1} (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.setLike.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) l (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u1), succ u2} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (a : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) a) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 v) l) x)))
Case conversion may be inaccurate. Consider using '#align finsupp.mem_span_image_iff_total Finsupp.mem_span_image_iff_totalₓ'. -/
theorem mem_span_image_iff_total {s : Set α} {x : M} :
x ∈ span R (v '' s) ↔ ∃ l ∈ supported R R s, Finsupp.total α M R v l = x :=
@@ -1186,7 +1186,7 @@ variable (α) (M) (v)
lean 3 declaration is
forall (α : Type.{u1}) (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (v : α -> M) (s : Set.{u1} α), LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (coeSort.{succ (max u1 u3), succ (succ (max u1 u3))} (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) Type.{max u1 u3} (SetLike.hasCoeToSort.{max u1 u3, max u1 u3} (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R 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_inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s)) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u3, u2} R M _inst_1 _inst_3 _inst_4)) (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s))) (Submodule.addCommMonoid.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s)) (Submodule.addCommMonoid.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s))) (Submodule.module.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s)) (Submodule.module.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s)))
but is expected to have type
- forall (α : Type.{u1}) (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (v : α -> M) (s : Set.{u1} α), LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Subtype.{succ (max u1 u3)} (Finsupp.{u1, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (fun (x : Finsupp.{u1, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) => Membership.mem.{max u1 u3, max u1 u3} (Finsupp.{u1, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (Submodule.{u3, max u3 u1} R (Finsupp.{u1, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (SetLike.instMembership.{max u1 u3, max u1 u3} (Submodule.{u3, max u3 u1} R (Finsupp.{u1, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (Finsupp.{u1, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (Submodule.instSetLikeSubmodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)))) x (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u3, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s)))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s)))
+ forall (α : Type.{u1}) (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (v : α -> M) (s : Set.{u1} α), LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Subtype.{succ (max u1 u3)} (Finsupp.{u1, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (fun (x : Finsupp.{u1, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) => Membership.mem.{max u1 u3, max u1 u3} (Finsupp.{u1, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (Submodule.{u3, max u3 u1} R (Finsupp.{u1, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (SetLike.instMembership.{max u1 u3, max u1 u3} (Submodule.{u3, max u3 u1} R (Finsupp.{u1, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (Finsupp.{u1, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (Submodule.setLike.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)))) x (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u3, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s)))) (Submodule.addCommMonoid.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s)) (Submodule.addCommMonoid.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s))) (Submodule.module.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s)) (Submodule.module.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s)))
Case conversion may be inaccurate. Consider using '#align finsupp.total_on Finsupp.totalOnₓ'. -/
/-- `finsupp.total_on M v s` interprets `p : α →₀ R` as a linear combination of a
subset of the vectors in `v`, mapping it to the span of those vectors.
@@ -1204,7 +1204,7 @@ variable {α} {M} {v}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {v : α -> M} (s : Set.{u1} α), Eq.{succ u2} (Submodule.{u3, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u3, u2} R M _inst_1 _inst_3 _inst_4)) (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s))) _inst_1 (Submodule.addCommMonoid.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s))) (Submodule.module.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s)))) (LinearMap.range.{u3, u3, max u1 u3, u2, max (max u1 u3) u2} R R (coeSort.{succ (max u1 u3), succ (succ (max u1 u3))} (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) Type.{max u1 u3} (SetLike.hasCoeToSort.{max u1 u3, max u1 u3} (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) (Submodule.setLike.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)))) (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s)) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u3, u2} R M _inst_1 _inst_3 _inst_4)) (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s))) _inst_1 _inst_1 (Submodule.addCommMonoid.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s)) (Submodule.addCommMonoid.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s))) (Submodule.module.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s)) (Submodule.module.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (coeSort.{succ (max u1 u3), succ (succ (max u1 u3))} (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) Type.{max u1 u3} (SetLike.hasCoeToSort.{max u1 u3, max u1 u3} (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) (Submodule.setLike.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)))) (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s)) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u3, u2} R M _inst_1 _inst_3 _inst_4)) (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s))) (Submodule.addCommMonoid.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R 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but is expected to have type
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u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))) (LinearMap.range.{u1, u1, max u3 u1, u2, max (max u3 u2) u1} R R (Subtype.{succ (max u3 u1)} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (fun (x : Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) => Membership.mem.{max u3 u1, max u3 u1} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.instSetLikeSubmodule.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R 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_inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))) _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))) (Submodule.instTopSubmodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))) _inst_1 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+ forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {v : α -> M} (s : Set.{u3} α), Eq.{succ u2} (Submodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (Submodule.module.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))) (LinearMap.range.{u1, u1, max u3 u1, u2, max (max u3 u2) u1} R R (Subtype.{succ (max u3 u1)} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (fun (x : Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) => Membership.mem.{max u3 u1, max u3 u1} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{max u3 u1, max u3 u1} (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.setLike.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) x (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))) _inst_1 _inst_1 (Submodule.addCommMonoid.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (Submodule.module.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Submodule.module.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Subtype.{succ (max u3 u1)} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (fun (x : Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) => Membership.mem.{max u3 u1, max u3 u1} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{max u3 u1, max u3 u1} (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.setLike.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) x (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))) (Submodule.addCommMonoid.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (Submodule.module.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Submodule.module.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u3 u1, u2} R R (Subtype.{succ (max u3 u1)} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (fun (x : Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) => Membership.mem.{max u3 u1, max u3 u1} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{max u3 u1, max u3 u1} (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.setLike.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) x (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))) _inst_1 _inst_1 (Submodule.addCommMonoid.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (Submodule.module.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Submodule.module.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.totalOn.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 v s)) (Top.top.{u2} (Submodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (Submodule.module.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))) (Submodule.instTopSubmodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (Submodule.module.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))))
Case conversion may be inaccurate. Consider using '#align finsupp.total_on_range Finsupp.totalOn_rangeₓ'. -/
theorem totalOn_range (s : Set α) : (Finsupp.totalOn α M R v s).range = ⊤ :=
by
@@ -1334,7 +1334,7 @@ theorem domLCongr_single {α₁ : Type _} {α₂ : Type _} (e : α₁ ≃ α₂)
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {α' : Type.{u4}} (s : Set.{u1} α) (t : Set.{u4} α'), (Equiv.{succ u1, succ u4} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (coeSort.{succ u4, succ (succ u4)} (Set.{u4} α') Type.{u4} (Set.hasCoeToSort.{u4} α') t)) -> (LinearEquiv.{u3, u3, max u1 u2, max u4 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (coeSort.{succ (max u4 u2), succ (succ (max u4 u2))} (Submodule.{u3, max u4 u2} R (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4)) Type.{max u4 u2} (SetLike.hasCoeToSort.{max u4 u2, max u4 u2} (Submodule.{u3, max u4 u2} R (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u4 u2} R (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4))) (Finsupp.supported.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4 t)) (Submodule.addCommMonoid.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Submodule.addCommMonoid.{u3, max u4 u2} R (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4 t)) (Submodule.module.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Submodule.module.{u3, max u4 u2} R (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4 t)))
but is expected to have type
- forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {α' : Type.{u4}} (s : Set.{u1} α) (t : Set.{u4} α'), (Equiv.{succ u1, succ u4} (Set.Elem.{u1} α s) (Set.Elem.{u4} α' t)) -> (LinearEquiv.{u3, u3, max u1 u2, max u2 u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Subtype.{succ (max u1 u2)} (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u1 u2, max u1 u2} (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u3, max u2 u1} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u3, max u2 u1} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) x (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s))) (Subtype.{succ (max u2 u4)} (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u2 u4, max u2 u4} (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u3, max u2 u4} R (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u2 u4, max u2 u4} (Submodule.{u3, max u2 u4} R (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u3, max u2 u4} R (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4))) x (Finsupp.supported.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4 t))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, max u2 u4} R (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4 t)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, max u2 u4} R (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4 t)))
+ forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {α' : Type.{u4}} (s : Set.{u1} α) (t : Set.{u4} α'), (Equiv.{succ u1, succ u4} (Set.Elem.{u1} α s) (Set.Elem.{u4} α' t)) -> (LinearEquiv.{u3, u3, max u1 u2, max u2 u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Subtype.{succ (max u1 u2)} (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u1 u2, max u1 u2} (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u3, max u2 u1} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u3, max u2 u1} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) x (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s))) (Subtype.{succ (max u2 u4)} (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u2 u4, max u2 u4} (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u3, max u2 u4} R (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u2 u4, max u2 u4} (Submodule.{u3, max u2 u4} R (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.setLike.{u3, max u2 u4} R (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4))) x (Finsupp.supported.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4 t))) (Submodule.addCommMonoid.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Submodule.addCommMonoid.{u3, max u2 u4} R (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4 t)) (Submodule.module.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Submodule.module.{u3, max u2 u4} R (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4 t)))
Case conversion may be inaccurate. Consider using '#align finsupp.congr Finsupp.congrₓ'. -/
/-- An equivalence of sets induces a linear equivalence of `finsupp`s supported on those sets. -/
noncomputable def congr {α' : Type _} (s : Set α) (t : Set α') (e : s ≃ t) :
@@ -1821,7 +1821,7 @@ variable {v} {x : M}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] {v : α -> M} {x : M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u3, u2} R M _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u3, u2} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u3, u2} R M _inst_2 _inst_3 _inst_4)) x (Submodule.span.{u3, u2} R M _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u1} M α v))) (Exists.{max (succ u1) (succ u3)} (α -> R) (fun (c : α -> R) => Eq.{succ u2} M (Finset.sum.{u2, u1} M α _inst_3 (Finset.univ.{u1} α _inst_1) (fun (i : α) => SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (c i) (v i))) x))
but is expected to have type
- forall {α : Type.{u1}} {M : Type.{u3}} (R : Type.{u2}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_2 _inst_3] {v : α -> M} {x : M}, Iff (Membership.mem.{u3, u3} M (Submodule.{u2, u3} R M _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R M _inst_2 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u3} R M _inst_2 _inst_3 _inst_4)) x (Submodule.span.{u2, u3} R M _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u1} M α v))) (Exists.{max (succ u1) (succ u2)} (α -> R) (fun (c : α -> R) => Eq.{succ u3} M (Finset.sum.{u3, u1} M α _inst_3 (Finset.univ.{u1} α _inst_1) (fun (i : α) => HSMul.hSMul.{u2, u3, u3} R M M (instHSMul.{u2, u3} R M (SMulZeroClass.toSMul.{u2, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u2, u3} R M _inst_2 _inst_3 _inst_4))))) (c i) (v i))) x))
+ forall {α : Type.{u1}} {M : Type.{u3}} (R : Type.{u2}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_2 _inst_3] {v : α -> M} {x : M}, Iff (Membership.mem.{u3, u3} M (Submodule.{u2, u3} R M _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u2, u3} R M _inst_2 _inst_3 _inst_4)) x (Submodule.span.{u2, u3} R M _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u1} M α v))) (Exists.{max (succ u1) (succ u2)} (α -> R) (fun (c : α -> R) => Eq.{succ u3} M (Finset.sum.{u3, u1} M α _inst_3 (Finset.univ.{u1} α _inst_1) (fun (i : α) => HSMul.hSMul.{u2, u3, u3} R M M (instHSMul.{u2, u3} R M (SMulZeroClass.toSMul.{u2, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u2, u3} R M _inst_2 _inst_3 _inst_4))))) (c i) (v i))) x))
Case conversion may be inaccurate. Consider using '#align mem_span_range_iff_exists_fun mem_span_range_iff_exists_funₓ'. -/
/-- An element `x` lies in the span of `v` iff it can be written as sum `∑ cᵢ • vᵢ = x`.
-/
@@ -1864,7 +1864,7 @@ variable (R)
lean 3 declaration is
forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (w : Set.{u2} M), (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w)) -> (Finsupp.{u2, u1} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) w) R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))
but is expected to have type
- forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (w : Set.{u2} M), (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w))) -> (Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))
+ forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (w : Set.{u2} M), (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w))) -> (Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))
Case conversion may be inaccurate. Consider using '#align span.repr Span.reprₓ'. -/
/-- Pick some representation of `x : span R w` as a linear combination in `w`,
using the axiom of choice.
@@ -1877,7 +1877,7 @@ irreducible_def Span.repr (w : Set M) (x : span R w) : w →₀ R :=
lean 3 declaration is
forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {w : Set.{u2} M} (x : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w)), Eq.{succ u2} M (coeFn.{max (succ (max u2 u1)) (succ u2), max (succ (max u2 u1)) (succ u2)} (LinearMap.{u1, u1, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) w) R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (Finsupp.addCommMonoid.{u2, u1} 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(Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w)) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w)) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w)) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w)) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w)))))) x)
but is expected to have type
- forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {w : Set.{u2} M} (x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) (Span.repr.{u1, u2} R M _inst_1 _inst_2 _inst_3 w x)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} (Set.Elem.{u2} M w) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} (Set.Elem.{u2} M w) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) (Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u2} R R (Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} (Set.Elem.{u2} M w) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} (Set.Elem.{u2} M w) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} (Set.Elem.{u2} M w) M R _inst_1 _inst_2 _inst_3 (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x w))) (Span.repr.{u1, u2} R M _inst_1 _inst_2 _inst_3 w x)) (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w))) x)
+ forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {w : Set.{u2} M} (x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) (Span.repr.{u1, u2} R M _inst_1 _inst_2 _inst_3 w x)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} (Set.Elem.{u2} M w) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} (Set.Elem.{u2} M w) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) (Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u2} R R (Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} (Set.Elem.{u2} M w) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} (Set.Elem.{u2} M w) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} (Set.Elem.{u2} M w) M R _inst_1 _inst_2 _inst_3 (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x w))) (Span.repr.{u1, u2} R M _inst_1 _inst_2 _inst_3 w x)) (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w))) x)
Case conversion may be inaccurate. Consider using '#align span.finsupp_total_repr Span.finsupp_total_reprₓ'. -/
@[simp]
theorem Span.finsupp_total_repr {w : Set M} (x : span R w) :
@@ -1893,7 +1893,7 @@ end
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Type.{u3}} {β : Type.{u4}} [_inst_6 : Zero.{u4} β] (S : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (f : Finsupp.{u3, u4} ι β _inst_6) (g : ι -> β -> M), (forall (c : ι), (Ne.{succ u4} β (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (Finsupp.{u3, u4} ι β _inst_6) (fun (_x : Finsupp.{u3, u4} ι β _inst_6) => ι -> β) (Finsupp.coeFun.{u3, u4} ι β _inst_6) f c) (OfNat.ofNat.{u4} β 0 (OfNat.mk.{u4} β 0 (Zero.zero.{u4} β _inst_6)))) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (g c (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (Finsupp.{u3, u4} ι β _inst_6) (fun (_x : Finsupp.{u3, u4} ι β _inst_6) => ι -> β) (Finsupp.coeFun.{u3, u4} ι β _inst_6) f c)) S)) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Finsupp.sum.{u3, u4, u2} ι β M _inst_6 _inst_2 f g) S)
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Type.{u4}} {β : Type.{u3}} [_inst_6 : Zero.{u3} β] (S : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (f : Finsupp.{u4, u3} ι β _inst_6) (g : ι -> β -> M), (forall (c : ι), (Ne.{succ u3} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => β) c) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Finsupp.{u4, u3} ι β _inst_6) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => β) _x) (Finsupp.funLike.{u4, u3} ι β _inst_6) f c) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => β) c) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => β) c) _inst_6))) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) (g c (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Finsupp.{u4, u3} ι β _inst_6) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => β) _x) (Finsupp.funLike.{u4, u3} ι β _inst_6) f c)) S)) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) (Finsupp.sum.{u4, u3, u1} ι β M _inst_6 _inst_2 f g) S)
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Type.{u4}} {β : Type.{u3}} [_inst_6 : Zero.{u3} β] (S : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (f : Finsupp.{u4, u3} ι β _inst_6) (g : ι -> β -> M), (forall (c : ι), (Ne.{succ u3} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => β) c) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Finsupp.{u4, u3} ι β _inst_6) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => β) _x) (Finsupp.funLike.{u4, u3} ι β _inst_6) f c) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => β) c) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => β) c) _inst_6))) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) (g c (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Finsupp.{u4, u3} ι β _inst_6) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => β) _x) (Finsupp.funLike.{u4, u3} ι β _inst_6) f c)) S)) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) (Finsupp.sum.{u4, u3, u1} ι β M _inst_6 _inst_2 f g) S)
Case conversion may be inaccurate. Consider using '#align submodule.finsupp_sum_mem Submodule.finsupp_sum_memₓ'. -/
protected theorem Submodule.finsupp_sum_mem {ι β : Type _} [Zero β] (S : Submodule R M) (f : ι →₀ β)
(g : ι → β → M) (h : ∀ c, f c ≠ 0 → g c (f c) ∈ S) : f.Sum g ∈ S :=
@@ -1915,7 +1915,7 @@ theorem LinearMap.map_finsupp_total (f : M →ₗ[R] N) {ι : Type _} {g : ι
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Type.{u3}} (p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) {m : M}, (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m (supᵢ.{u2, succ u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) -> (Exists.{succ u3} (Finset.{u3} ι) (fun (s : Finset.{u3} ι) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m (supᵢ.{u2, succ u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => supᵢ.{u2, 0} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) (fun (H : Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) => p i)))))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Type.{u3}} (p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) {m : M}, (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m (supᵢ.{u1, succ u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) -> (Exists.{succ u3} (Finset.{u3} ι) (fun (s : Finset.{u3} ι) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m (supᵢ.{u1, succ u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => supᵢ.{u1, 0} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) (fun (H : Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) => p i)))))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Type.{u3}} (p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) {m : M}, (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m (supᵢ.{u1, succ u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) -> (Exists.{succ u3} (Finset.{u3} ι) (fun (s : Finset.{u3} ι) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m (supᵢ.{u1, succ u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => supᵢ.{u1, 0} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) (fun (H : Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) => p i)))))
Case conversion may be inaccurate. Consider using '#align submodule.exists_finset_of_mem_supr Submodule.exists_finset_of_mem_supᵢₓ'. -/
theorem Submodule.exists_finset_of_mem_supᵢ {ι : Sort _} (p : ι → Submodule R M) {m : M}
(hm : m ∈ ⨆ i, p i) : ∃ s : Finset ι, m ∈ ⨆ i ∈ s, p i :=
@@ -1931,7 +1931,7 @@ theorem Submodule.exists_finset_of_mem_supᵢ {ι : Sort _} (p : ι → Submodul
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Type.{u3}} {p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)} {m : M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m (supᵢ.{u2, succ u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) (Exists.{succ u3} (Finset.{u3} ι) (fun (s : Finset.{u3} ι) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m (supᵢ.{u2, succ u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => supᵢ.{u2, 0} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) (fun (H : Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) => p i)))))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Type.{u3}} {p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)} {m : M}, Iff (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m (supᵢ.{u1, succ u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) (Exists.{succ u3} (Finset.{u3} ι) (fun (s : Finset.{u3} ι) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m (supᵢ.{u1, succ u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => supᵢ.{u1, 0} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) (fun (H : Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) => p i)))))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Type.{u3}} {p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)} {m : M}, Iff (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m (supᵢ.{u1, succ u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) (Exists.{succ u3} (Finset.{u3} ι) (fun (s : Finset.{u3} ι) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m (supᵢ.{u1, succ u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => supᵢ.{u1, 0} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) (fun (H : Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) => p i)))))
Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_iff_exists_finset Submodule.mem_supᵢ_iff_exists_finsetₓ'. -/
/-- `submodule.exists_finset_of_mem_supr` as an `iff` -/
theorem Submodule.mem_supᵢ_iff_exists_finset {ι : Sort _} {p : ι → Submodule R M} {m : M} :
@@ -1940,12 +1940,7 @@ theorem Submodule.mem_supᵢ_iff_exists_finset {ι : Sort _} {p : ι → Submodu
supᵢ_mono (fun i => (supᵢ_const_le : _ ≤ p i)) hs⟩
#align submodule.mem_supr_iff_exists_finset Submodule.mem_supᵢ_iff_exists_finset
-/- warning: mem_span_finset -> mem_span_finset is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Finset.{u2} M} {x : M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} M) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} M) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} M) (Set.{u2} M) (Finset.Set.hasCoeT.{u2} M))) s))) (Exists.{max (succ u2) (succ u1)} (M -> R) (fun (f : M -> R) => Eq.{succ u2} M (Finset.sum.{u2, u2} M M _inst_2 s (fun (i : M) => SMul.smul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (f i) i)) x))
-but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Finset.{u2} M} {x : M}, Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Finset.toSet.{u2} M s))) (Exists.{max (succ u1) (succ u2)} (M -> R) (fun (f : M -> R) => Eq.{succ u2} M (Finset.sum.{u2, u2} M M _inst_2 s (fun (i : M) => HSMul.hSMul.{u1, u2, u2} R M M (instHSMul.{u1, u2} R M (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) (f i) i)) x))
-Case conversion may be inaccurate. Consider using '#align mem_span_finset mem_span_finsetₓ'. -/
+#print mem_span_finset /-
theorem mem_span_finset {s : Finset M} {x : M} :
x ∈ span R (↑s : Set M) ↔ ∃ f : M → R, (∑ i in s, f i • i) = x :=
⟨fun hx =>
@@ -1955,12 +1950,13 @@ theorem mem_span_finset {s : Finset M} {x : M} :
⟨v, hvx ▸ (Finsupp.total_apply_of_mem_supported _ hvs).symm⟩,
fun ⟨f, hf⟩ => hf ▸ sum_mem fun i hi => smul_mem _ _ <| subset_span hi⟩
#align mem_span_finset mem_span_finset
+-/
/- warning: mem_span_set -> mem_span_set is a dubious translation:
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {m : M} {s : Set.{u2} M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) (Exists.{max (succ u2) (succ u1)} (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (fun (c : Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) => And (HasSubset.Subset.{u2} (Set.{u2} M) (Set.hasSubset.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} M) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} M) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} M) (Set.{u2} M) (Finset.Set.hasCoeT.{u2} M))) (Finsupp.support.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) c)) s) (Eq.{succ u2} M (Finsupp.sum.{u2, u1, u2} M R M (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 c (fun (mi : M) (r : R) => SMul.smul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) r mi)) m)))
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {m : M} {s : Set.{u2} M}, Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) (Exists.{max (succ u1) (succ u2)} (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (c : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => And (HasSubset.Subset.{u2} (Set.{u2} M) (Set.instHasSubsetSet.{u2} M) (Finset.toSet.{u2} M (Finsupp.support.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) c)) s) (Eq.{succ u2} M (Finsupp.sum.{u2, u1, u2} M R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) _inst_2 c (fun (mi : M) (r : R) => HSMul.hSMul.{u1, u2, u2} R M M (instHSMul.{u1, u2} R M (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) r mi)) m)))
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {m : M} {s : Set.{u2} M}, Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) (Exists.{max (succ u1) (succ u2)} (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (c : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => And (HasSubset.Subset.{u2} (Set.{u2} M) (Set.instHasSubsetSet.{u2} M) (Finset.toSet.{u2} M (Finsupp.support.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) c)) s) (Eq.{succ u2} M (Finsupp.sum.{u2, u1, u2} M R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) _inst_2 c (fun (mi : M) (r : R) => HSMul.hSMul.{u1, u2, u2} R M M (instHSMul.{u1, u2} R M (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) r mi)) m)))
Case conversion may be inaccurate. Consider using '#align mem_span_set mem_span_setₓ'. -/
/-- An element `m ∈ M` is contained in the `R`-submodule spanned by a set `s ⊆ M`, if and only if
`m` can be written as a finite `R`-linear combination of elements of `s`.
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d
@@ -368,7 +368,7 @@ theorem supported_eq_span_single (s : Set α) :
exact single_mem_supported R 1 hp
· rw [← l.sum_single]
refine' sum_mem fun i il => _
- convert @smul_mem R (α →₀ R) _ _ _ _ (single i 1) (l i) _
+ convert@smul_mem R (α →₀ R) _ _ _ _ (single i 1) (l i) _
· simp
apply subset_span
apply Set.mem_image_of_mem _ (hl il)
@@ -576,7 +576,7 @@ variable (S) [Module S N] [SMulCommClass R S N]
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toHasSmul.{u4, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u4, u3} R N (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u5, u3} S N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u5, u3} S N (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))], LinearEquiv.{u5, u5, max u1 u2 u3, max (max u1 u2) u3} S S _inst_2 _inst_2 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2) (α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u1, max u2 u3} α (fun (ᾰ : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.Function.module.{u1, u5, max u2 u3} α S (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.module.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.module.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)
but is expected to have type
- forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toSMul.{u4, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u4, u3} R N (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u5, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} S N (MonoidWithZero.toZero.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))], LinearEquiv.{u5, u5, max (max u1 u2) u3, max u3 u2 u1} S S _inst_2 _inst_2 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2) (α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u4, u4, max u2 u1, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u1, max u2 u3} α (fun (ᾰ : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.module.{u1, max u2 u3, u5} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)
+ forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toSMul.{u4, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u4, u3} R N (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u5, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} S N (MonoidWithZero.toZero.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))], LinearEquiv.{u5, u5, max (max u1 u2) u3, max u3 u2 u1} S S _inst_2 _inst_2 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2) (α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u4, u4, max u2 u1, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u1, max u2 u3} α (fun (ᾰ : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.module.{u1, max u2 u3, u5} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)
Case conversion may be inaccurate. Consider using '#align finsupp.lsum Finsupp.lsumₓ'. -/
/-- Lift a family of linear maps `M →ₗ[R] N` indexed by `x : α` to a linear map from `α →₀ M` to
`N` using `finsupp.sum`. This is an upgraded version of `finsupp.lift_add_hom`.
@@ -608,7 +608,7 @@ def lsum : (α → M →ₗ[R] N) ≃ₗ[S] (α →₀ M) →ₗ[R] N
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toHasSmul.{u4, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u4, u3} R N (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u5, u3} S N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u5, u3} S N (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)), Eq.{max (max (succ u1) (succ u2)) (succ u3)} ((fun (_x : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) => (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) -> N) (coeFn.{max (succ (max u1 u2 u3)) (succ (max (max u1 u2) u3)), max (succ (max u1 u2 u3)) (succ (max (max u1 u2) u3))} (LinearEquiv.{u5, u5, max u1 u2 u3, max (max u1 u2) u3} S S _inst_2 _inst_2 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S 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_inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6)) (LinearEquiv.hasCoeToFun.{u5, u5, max u1 u2 u3, max (max u1 u2) u3} S S (α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u1, max u2 u3} α (fun (ᾰ : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.Function.module.{u1, u5, max u2 u3} α S (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.module.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.module.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2)) (Finsupp.lsum.{u1, u2, u3, u4, u5} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f)) (fun (d : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) => Finsupp.sum.{u1, u2, u3} α M N (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_5 d (fun (i : α) => coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (_x : LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) => M -> N) (LinearMap.hasCoeToFun.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (f i)))
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u4}} {N : Type.{u3}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u3} R S N (SMulZeroClass.toSMul.{u5, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)), Eq.{max (max (succ u2) (succ u4)) (succ u3)} (forall (a : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) a) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) 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(LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R 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_inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M 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(LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2} S S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f)) (fun (d : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => Finsupp.sum.{u2, u4, u3} α M ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) d) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) _inst_5 d (fun (i : α) => FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f i)))
+ forall {α : Type.{u2}} {M : Type.{u4}} {N : Type.{u3}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u3} R S N (SMulZeroClass.toSMul.{u5, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)), Eq.{max (max (succ u2) (succ u4)) (succ u3)} (forall (a : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) a) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) f) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (fun (_x : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (fun (_x : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _x) (SMulHomClass.toFunLike.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R 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_inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M 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(RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f)) (fun (d : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => Finsupp.sum.{u2, u4, u3} α M ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) d) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) _inst_5 d (fun (i : α) => FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f i)))
Case conversion may be inaccurate. Consider using '#align finsupp.coe_lsum Finsupp.coe_lsumₓ'. -/
@[simp]
theorem coe_lsum (f : α → M →ₗ[R] N) : (lsum S f : (α →₀ M) → N) = fun d => d.Sum fun i => f i :=
@@ -619,7 +619,7 @@ theorem coe_lsum (f : α → M →ₗ[R] N) : (lsum S f : (α →₀ M) → N) =
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toHasSmul.{u4, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u4, u3} R N (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u5, u3} S N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u5, u3} S N (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (l : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))), Eq.{succ u3} N (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (fun (_x : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 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_inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u1, max u2 u3} α (fun (ᾰ : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.Function.module.{u1, u5, max u2 u3} α S (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.module.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.module.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2)) (Finsupp.lsum.{u1, u2, u3, u4, u5} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f) l) (Finsupp.sum.{u1, u2, u3} α M N (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_5 l (fun (b : α) => coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (_x : LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) => M -> N) (LinearMap.hasCoeToFun.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (f b)))
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u4}} {N : Type.{u3}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u3} R S N (SMulZeroClass.toSMul.{u5, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (l : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) l) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), succ u3} ((fun 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_inst_2 _inst_9 _inst_10)) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (fun (_x : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _x) (SMulHomClass.toFunLike.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} 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_inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R 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_inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M 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(AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2} S S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f) l) (Finsupp.sum.{u2, u4, u3} α M N (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) _inst_5 l (fun (b : α) => FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f b)))
+ forall {α : Type.{u2}} {M : Type.{u4}} {N : Type.{u3}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u3} R S N (SMulZeroClass.toSMul.{u5, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (l : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) l) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) f) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (fun (_x : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (fun (_x : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _x) (SMulHomClass.toFunLike.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} 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_inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R 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(RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f) l) (Finsupp.sum.{u2, u4, u3} α M N (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) _inst_5 l (fun (b : α) => FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f b)))
Case conversion may be inaccurate. Consider using '#align finsupp.lsum_apply Finsupp.lsum_applyₓ'. -/
theorem lsum_apply (f : α → M →ₗ[R] N) (l : α →₀ M) : Finsupp.lsum S f l = l.Sum fun b => f b :=
rfl
@@ -629,7 +629,7 @@ theorem lsum_apply (f : α → M →ₗ[R] N) (l : α →₀ M) : Finsupp.lsum S
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toHasSmul.{u4, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u4, u3} R N (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u5, u3} S N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u5, u3} S N (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (i : α) (m : M), Eq.{succ u3} N (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (fun (_x : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) => (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M 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(AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (i : α) (m : M), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) (Finsupp.single.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) i m)) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), succ u3} 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_inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => 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(Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 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(AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 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R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2} S S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f) (Finsupp.single.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) i m)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f i) m)
+ forall {α : Type.{u2}} {M : Type.{u4}} {N : Type.{u3}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u3} R S N (SMulZeroClass.toSMul.{u5, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (i : α) (m : M), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) (Finsupp.single.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) i m)) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) f) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (fun (_x : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (fun (_x : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _x) (SMulHomClass.toFunLike.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M 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(RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M 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u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) 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_inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2} S S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f) (Finsupp.single.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) i m)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f i) m)
Case conversion may be inaccurate. Consider using '#align finsupp.lsum_single Finsupp.lsum_singleₓ'. -/
theorem lsum_single (f : α → M →ₗ[R] N) (i : α) (m : M) :
Finsupp.lsum S f (Finsupp.single i m) = f i m :=
@@ -640,7 +640,7 @@ theorem lsum_single (f : α → M →ₗ[R] N) (i : α) (m : M) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toHasSmul.{u4, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u4, u3} R N (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u5, u3} S N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u5, u3} S N (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))] (f : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (x : α), Eq.{max (succ u2) (succ u3)} (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (coeFn.{max (succ (max (max u1 u2) u3)) (succ (max u1 u2 u3)), max (succ (max (max u1 u2) u3)) (succ (max u1 u2 u3))} (LinearEquiv.{u5, u5, max (max u1 u2) u3, max u1 u2 u3} S S _inst_2 _inst_2 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2) (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M 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(AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.Function.module.{u1, u5, max u2 u3} α S (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.module.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.module.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2) (Finsupp.lsum.{u1, u2, u3, u4, u5} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10)) f x) (LinearMap.comp.{u4, u4, u4, u2, max u1 u2, u3} R R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 _inst_4 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomCompTriple.right_ids.{u4, u4} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) f (Finsupp.lsingle.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4 x))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u4}} {N : Type.{u2}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : Module.{u5, u2} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u2} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u2} R S N (SMulZeroClass.toSMul.{u5, u2} R N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u2} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u2} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (Module.toMulActionWithZero.{u5, u2} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u2} S N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u2} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u2} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (Module.toMulActionWithZero.{u1, u2} S N _inst_2 _inst_5 _inst_9))))] (f : LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (x : α), Eq.{max (succ u4) (succ u2)} (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (max (succ u2) (succ u4)) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (fun (_x : LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) => α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _x) (SMulHomClass.toFunLike.{max (max u2 u4) u3, u1, max (max u2 u4) u3, max (max u2 u4) u3} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (SMulZeroClass.toSMul.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (SMulZeroClass.toSMul.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u4) u3, u1, max (max u2 u4) u3, max (max u2 u4) u3} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u2 u4) u3, max (max u2 u4) u3, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3, max (max u2 u4) u3} S S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) _inst_2 _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (LinearEquiv.symm.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (ᾰ : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (Finsupp.lsum.{u3, u4, u2, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10)) f x) (LinearMap.comp.{u5, u5, u5, u4, max u3 u4, u2} R R R M (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 _inst_4 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHomCompTriple.ids.{u5, u5} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) f (Finsupp.lsingle.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4 x))
+ forall {α : Type.{u3}} {M : Type.{u4}} {N : Type.{u2}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : Module.{u5, u2} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u2} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u2} R S N (SMulZeroClass.toSMul.{u5, u2} R N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u2} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u2} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (Module.toMulActionWithZero.{u5, u2} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u2} S N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u2} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u2} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (Module.toMulActionWithZero.{u1, u2} S N _inst_2 _inst_5 _inst_9))))] (f : LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (x : α), Eq.{max (succ u4) (succ u2)} (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (max (succ u2) (succ u4)) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (fun (_x : LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) => α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _x) (SMulHomClass.toFunLike.{max (max u2 u4) u3, u1, max (max u2 u4) u3, max (max u2 u4) u3} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (SMulZeroClass.toSMul.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (SMulZeroClass.toSMul.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u4) u3, u1, max (max u2 u4) u3, max (max u2 u4) u3} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u2 u4) u3, max (max u2 u4) u3, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R 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(Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4473 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (LinearEquiv.symm.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (ᾰ : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 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(RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (Finsupp.lsum.{u3, u4, u2, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10)) f x) (LinearMap.comp.{u5, u5, u5, u4, max u3 u4, u2} R R R M (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 _inst_4 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHomCompTriple.ids.{u5, u5} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) f (Finsupp.lsingle.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4 x))
Case conversion may be inaccurate. Consider using '#align finsupp.lsum_symm_apply Finsupp.lsum_symm_applyₓ'. -/
theorem lsum_symm_apply (f : (α →₀ M) →ₗ[R] N) (x : α) : (lsum S).symm f x = f.comp (lsingle x) :=
rfl
@@ -670,7 +670,7 @@ noncomputable def lift : (X → M) ≃+ ((X →₀ R) →ₗ[R] M) :=
lean 3 declaration is
forall (M : Type.{u1}) (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u3}) (f : LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (x : X), Eq.{succ u1} M (coeFn.{max (succ (max (max u3 u2) u1)) (succ 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(NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.instAdd.{u3, u1} X (fun (ᾰ : X) => M) (fun (i : X) => AddZeroClass.toHasAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (fun (_x : AddEquiv.{max (max u3 u2) u1, max u3 u1} (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (X -> M) (LinearMap.hasAdd.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.instAdd.{u3, u1} X (fun (ᾰ : X) => M) (fun (i : X) => AddZeroClass.toHasAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) => (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) -> X -> M) (AddEquiv.hasCoeToFun.{max (max u3 u2) u1, max u3 u1} (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (X -> M) (LinearMap.hasAdd.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.instAdd.{u3, u1} X (fun (ᾰ : X) => M) (fun (i : X) => AddZeroClass.toHasAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (AddEquiv.symm.{max u3 u1, max (max u3 u2) u1} (X -> M) (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (ᾰ : X) => M) (fun (i : X) => AddZeroClass.toHasAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.hasAdd.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.lift.{u1, u2, u3} M R _inst_1 _inst_3 _inst_4 X)) f x) (coeFn.{max (succ (max u3 u2)) (succ u1), max (succ (max u3 u2)) (succ u1)} (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) => (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f (Finsupp.single.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) x (OfNat.ofNat.{u2} R 1 (OfNat.mk.{u2} R 1 (One.one.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))))))
but is expected to have type
- forall (M : Type.{u1}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_3] (X : Type.{u2}) (f : LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (x : X), Eq.{succ u1} M (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2)} (AddEquiv.{max (max u1 u3) u2, max u1 u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (LinearMap.instAddLinearMap.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.instAdd.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4940 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => X -> M) _x) (AddHomClass.toFunLike.{max (max u1 u3) u2, max (max u1 u3) u2, max u1 u2} (AddEquiv.{max (max u1 u3) u2, max u1 u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (LinearMap.instAddLinearMap.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.instAdd.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4940 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (AddZeroClass.toAdd.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddMonoid.toAddZeroClass.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (AddZeroClass.toAdd.{max u1 u2} (X -> M) (Pi.addZeroClass.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4940 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (AddMonoidHomClass.toAddHomClass.{max (max u1 u3) u2, max (max u1 u3) u2, max u1 u2} (AddEquiv.{max (max u1 u3) u2, max u1 u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (LinearMap.instAddLinearMap.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.instAdd.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4940 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (AddMonoid.toAddZeroClass.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Pi.addZeroClass.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4940 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddEquivClass.instAddMonoidHomClass.{max (max u1 u3) u2, max (max u1 u3) u2, max u1 u2} (AddEquiv.{max (max u1 u3) u2, max u1 u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (LinearMap.instAddLinearMap.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.instAdd.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4940 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (AddMonoid.toAddZeroClass.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Pi.addZeroClass.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4940 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddEquiv.instAddEquivClassAddEquiv.{max (max u1 u3) u2, max u1 u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (LinearMap.instAddLinearMap.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.instAdd.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4940 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))) (AddEquiv.symm.{max u1 u2, max (max u1 u3) u2} (X -> M) (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lift.{u1, u3, u2} M R _inst_1 _inst_3 _inst_4 X)) f x) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R 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+ forall (M : Type.{u1}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_3] (X : Type.{u2}) (f : LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (x : X), Eq.{succ u1} M (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2)} (AddEquiv.{max (max u1 u3) u2, 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u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (LinearMap.instAddLinearMap.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.instAdd.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4991 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (AddZeroClass.toAdd.{max (max u1 u3) u2} (LinearMap.{u3, 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R 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Case conversion may be inaccurate. Consider using '#align finsupp.lift_symm_apply Finsupp.lift_symm_applyₓ'. -/
@[simp]
theorem lift_symm_apply (f) (x) : ((lift M R X).symm f) x = f (single x 1) :=
@@ -681,7 +681,7 @@ theorem lift_symm_apply (f) (x) : ((lift M R X).symm f) x = f (single x 1) :=
lean 3 declaration is
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(Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) 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(NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) => (X -> M) -> (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R 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(Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (ᾰ : X) => M) (fun (i : X) => AddZeroClass.toHasAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.hasAdd.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.lift.{u1, u2, u3} M R _inst_1 _inst_3 _inst_4 X) f) g) (Finsupp.sum.{u3, u2, u1} X R M (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 g (fun (x : X) (r : R) => SMul.smul.{u2, u1} R M (SMulZeroClass.toHasSmul.{u2, u1} R M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u1} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4)))) r (f x)))
but is expected to have type
- forall (M : Type.{u1}) (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u3}) (f : X -> M) (g : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) g) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : X -> M) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) f) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (max (succ u1) (succ u2)) (succ u3)} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4940 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (fun (_x : X -> M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : X -> M) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) _x) (AddHomClass.toFunLike.{max (max u1 u2) u3, max u1 u3, max (max u1 u2) u3} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4940 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddZeroClass.toAdd.{max u1 u3} (X -> M) (Pi.addZeroClass.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4940 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (AddZeroClass.toAdd.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (AddMonoidHomClass.toAddHomClass.{max (max u1 u2) u3, max u1 u3, max (max u1 u2) u3} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4940 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.addZeroClass.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4940 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddEquivClass.instAddMonoidHomClass.{max (max u1 u2) u3, max u1 u3, max (max u1 u2) u3} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4940 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.addZeroClass.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4940 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddEquiv.instAddEquivClassAddEquiv.{max u1 u3, max (max u1 u2) u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4940 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (Finsupp.lift.{u1, u2, u3} M R _inst_1 _inst_3 _inst_4 X) f) g) (Finsupp.sum.{u3, u2, u1} X R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) _inst_3 g (fun (x : X) (r : R) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4))))) r (f x)))
+ forall (M : Type.{u1}) (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u3}) (f : X -> M) (g : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) g) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : X -> M) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) f) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (max (succ u1) (succ u2)) (succ u3)} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4991 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (fun (_x : X -> M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : X -> M) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) _x) (AddHomClass.toFunLike.{max (max u1 u2) u3, max u1 u3, max (max u1 u2) u3} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4991 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddZeroClass.toAdd.{max u1 u3} (X -> M) (Pi.addZeroClass.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4991 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (AddZeroClass.toAdd.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (AddMonoidHomClass.toAddHomClass.{max (max u1 u2) u3, max u1 u3, max (max u1 u2) u3} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4991 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.addZeroClass.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4991 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddEquivClass.instAddMonoidHomClass.{max (max u1 u2) u3, max u1 u3, max (max u1 u2) u3} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4991 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.addZeroClass.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4991 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddEquiv.instAddEquivClassAddEquiv.{max u1 u3, max (max u1 u2) u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4991 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (Finsupp.lift.{u1, u2, u3} M R _inst_1 _inst_3 _inst_4 X) f) g) (Finsupp.sum.{u3, u2, u1} X R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) _inst_3 g (fun (x : X) (r : R) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4))))) r (f x)))
Case conversion may be inaccurate. Consider using '#align finsupp.lift_apply Finsupp.lift_applyₓ'. -/
@[simp]
theorem lift_apply (f) (g) : ((lift M R X) f) g = g.Sum fun x r => r • f x :=
@@ -898,7 +898,7 @@ theorem total_single (c : R) (a : α) : Finsupp.total α M R v (single a c) = c
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (x : Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u1 u2} (α -> M) 0 (OfNat.mk.{max u1 u2} (α -> M) 0 (Zero.zero.{max u1 u2} (α -> M) (Pi.instZero.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))))))) x) (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))))))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u3 u1} (α -> M) 0 (Zero.toOfNat0.{max u3 u1} (α -> M) (Pi.instZero.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.6502 : α) => M) (fun (i : α) => AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) _inst_3))))
+ forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u3 u1} (α -> M) 0 (Zero.toOfNat0.{max u3 u1} (α -> M) (Pi.instZero.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.6553 : α) => M) (fun (i : α) => AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) _inst_3))))
Case conversion may be inaccurate. Consider using '#align finsupp.total_zero_apply Finsupp.total_zero_applyₓ'. -/
theorem total_zero_apply (x : α →₀ R) : (Finsupp.total α M R 0) x = 0 := by
simp [Finsupp.total_apply]
@@ -910,7 +910,7 @@ variable (α M)
lean 3 declaration is
forall (α : Type.{u1}) (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], Eq.{max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u1 u2} (α -> M) 0 (OfNat.mk.{max u1 u2} (α -> M) 0 (Zero.zero.{max u1 u2} (α -> M) (Pi.instZero.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))))))) (OfNat.ofNat.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) 0 (OfNat.mk.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) 0 (Zero.zero.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.hasZero.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))
but is expected to have type
- forall (α : Type.{u3}) (M : Type.{u2}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Eq.{max (max (succ u3) (succ u2)) (succ u1)} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u3 u2} (α -> M) 0 (Zero.toOfNat0.{max u3 u2} (α -> M) (Pi.instZero.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.6502 : α) => M) (fun (i : α) => AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))))) (OfNat.ofNat.{max (max u3 u2) u1} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) 0 (Zero.toOfNat0.{max (max u3 u2) u1} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (LinearMap.instZeroLinearMap.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))
+ forall (α : Type.{u3}) (M : Type.{u2}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Eq.{max (max (succ u3) (succ u2)) (succ u1)} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u3 u2} (α -> M) 0 (Zero.toOfNat0.{max u3 u2} (α -> M) (Pi.instZero.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.6553 : α) => M) (fun (i : α) => AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))))) (OfNat.ofNat.{max (max u3 u2) u1} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) 0 (Zero.toOfNat0.{max (max u3 u2) u1} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (LinearMap.instZeroLinearMap.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))
Case conversion may be inaccurate. Consider using '#align finsupp.total_zero Finsupp.total_zeroₓ'. -/
@[simp]
theorem total_zero : Finsupp.total α M R 0 = 0 :=
@@ -1749,7 +1749,7 @@ variable {S}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] {S : Type.{u4}} [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (f : α -> R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) => (α -> R) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (coeFn.{max (succ (max u1 u2)) (succ (max (max u1 u3) u2)), max (succ (max u1 u2)) (succ (max (max u1 u3) u2))} (LinearMap.{u4, u4, max u1 u2, max (max u1 u3) u2} S S _inst_5 _inst_5 (RingHom.id.{u4} S 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(Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) (fun (_x : LinearMap.{u4, u4, max u1 u2, max (max u1 u3) u2} S S _inst_5 _inst_5 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) => (α -> M) -> (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4)) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, max (max u1 u3) u2} S S (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) f) (Finset.sum.{u2, u1} M α _inst_3 (Finset.univ.{u1} α _inst_1) (fun (i : α) => SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (f i) (v i)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (f : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) f) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) v) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearMap.{u1, u1, max u3 u4, max u4 u3 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u3, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14077 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14077 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14077 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) f) (Finset.sum.{u4, u3} M α _inst_3 (Finset.univ.{u3} α _inst_1) (fun (i : α) => HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) (f i) (v i)))
+ forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M 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Case conversion may be inaccurate. Consider using '#align fintype.total_apply Fintype.total_applyₓ'. -/
theorem Fintype.total_apply (f) : Fintype.total R S v f = ∑ i, f i • v i :=
rfl
@@ -1759,7 +1759,7 @@ theorem Fintype.total_apply (f) : Fintype.total R S v f = ∑ i, f i • v i :=
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] {S : Type.{u4}} [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (i : α) (r : R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) => (α -> M) -> (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4)) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, max (max u1 u3) u2} S S (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) (Pi.single.{u1, u3} α (fun (ᾰ : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u1} α a b)) (fun (i : α) => MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) i r)) (SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) r (v i))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (i : α) (r : R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) (Pi.single.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) v) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearMap.{u1, u1, max u3 u4, max u4 u3 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R 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(i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14077 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14077 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) (Pi.single.{u3, u2} α (fun (ᾰ : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) r (v i))
+ forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (i : α) (r : R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) (Pi.single.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) v) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearMap.{u1, u1, max u3 u4, max u4 u3 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u3, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14128 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14128 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14128 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) (Pi.single.{u3, u2} α (fun (ᾰ : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) r (v i))
Case conversion may be inaccurate. Consider using '#align fintype.total_apply_single Fintype.total_apply_singleₓ'. -/
@[simp]
theorem Fintype.total_apply_single (i : α) (r : R) :
@@ -1775,7 +1775,7 @@ variable (S)
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] (S : Type.{u4}) [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (x : α -> R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))) M _inst_2 _inst_2 (Finsupp.addCommMonoid.{u1, 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(Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) x)
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (x : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) => M) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (α -> R) (fun (a : α -> R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> R) => Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) a) (SMulHomClass.toFunLike.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (α -> R) (AddMonoid.toZero.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (α -> R) (AddMonoid.toAddZeroClass.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (α -> R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u3 u2, max u3 u2, max u3 u2} R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) 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(a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (α -> R) (AddMonoid.toAddZeroClass.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (α -> R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u3 u2, max u3 u2, max u3 u2} R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u3 u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2)))))) (LinearEquiv.symm.{u2, u2, max u3 u2, max u3 u2} R R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (α -> R) _inst_2 _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (Finsupp.linearEquivFunOnFinite.{u2, u2, u3} R R α (Finite.of_fintype.{u3} α _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) _inst_2 (Semiring.toModule.{u2} R _inst_2))) x)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) v) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearMap.{u1, u1, max u3 u4, max u4 u3 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun 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(Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14077 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14077 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) x)
+ forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (x : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) => M) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (α -> R) (fun (a : α -> R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> R) => Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) a) (SMulHomClass.toFunLike.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (α -> R) (AddMonoid.toZero.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (α -> R) (AddMonoid.toAddZeroClass.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (α -> R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u3 u2, max u3 u2, max u3 u2} R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u3 u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2)))))) (LinearEquiv.symm.{u2, u2, max u3 u2, max u3 u2} R R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (α -> R) _inst_2 _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) _inst_2 (Semiring.toModule.{u2} R _inst_2))) x)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α 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_inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14128 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) x)
Case conversion may be inaccurate. Consider using '#align finsupp.total_eq_fintype_total_apply Finsupp.total_eq_fintype_total_applyₓ'. -/
theorem Finsupp.total_eq_fintype_total_apply (x : α → R) :
Finsupp.total α M R v ((Finsupp.linearEquivFunOnFinite R R α).symm x) = Fintype.total R S v x :=
@@ -1791,7 +1791,7 @@ theorem Finsupp.total_eq_fintype_total_apply (x : α → R) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] (S : Type.{u4}) [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (LinearMap.comp.{u3, u3, u3, max u1 u3, max u1 u3, u2} R R R (α -> R) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))) M _inst_2 _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHomCompTriple.right_ids.{u3, u3} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Finsupp.total.{u1, u2, u3} α M R _inst_2 _inst_3 _inst_4 v) (LinearEquiv.toLinearMap.{u3, u3, max u1 u3, max u1 u3} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHomInvPair.ids.{u3} R _inst_2) (RingHomInvPair.ids.{u3} R _inst_2) (α -> R) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))))) (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Pi.Function.module.{u1, 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(fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) => (α -> M) -> (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4)) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, max (max u1 u3) u2} S S (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)
but is expected to have type
- forall {α : Type.{u4}} {M : Type.{u3}} (R : Type.{u2}) [_inst_1 : Fintype.{u4} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u3} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u3} R S M (SMulZeroClass.toSMul.{u2, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u2, u3} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u3} S M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u1, u3} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (LinearMap.comp.{u2, u2, u2, max u4 u2, max u4 u2, u3} R R R (α -> R) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) M _inst_2 _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => 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(Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u4, max (max u2 u3) u4} S S (α -> M) (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u4, u3} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u4 u2, u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u4, u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14077 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u4 u2, u3} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u4, u3, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)
+ forall {α : Type.{u4}} {M : Type.{u3}} (R : Type.{u2}) [_inst_1 : Fintype.{u4} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u3} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u3} R S M (SMulZeroClass.toSMul.{u2, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u2, u3} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u3} S M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u1, u3} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (LinearMap.comp.{u2, u2, u2, max u4 u2, max u4 u2, u3} R R R (α -> R) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) M _inst_2 _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomCompTriple.ids.{u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Finsupp.total.{u4, u3, u2} α M R _inst_2 _inst_3 _inst_4 v) (LinearEquiv.toLinearMap.{u2, u2, max u4 u2, max u4 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u4, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (LinearEquiv.symm.{u2, u2, max u4 u2, max u4 u2} R R (Finsupp.{u4, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (α -> R) _inst_2 _inst_2 (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (Finsupp.linearEquivFunOnFinite.{u2, u2, u4} R R α (Finite.of_fintype.{u4} α _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) _inst_2 (Semiring.toModule.{u2} R _inst_2))))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), max (max (succ u2) (succ u3)) (succ u4)} (LinearMap.{u1, u1, max u4 u3, max u3 u4 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u4, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14128 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u4 u2, u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u4, u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14128 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u4 u2, u3} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u4, max (max u2 u3) u4} S S (α -> M) (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u4, u3} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u4 u2, u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u4, u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14128 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u4 u2, u3} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u4, u3, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)
Case conversion may be inaccurate. Consider using '#align finsupp.total_eq_fintype_total Finsupp.total_eq_fintype_totalₓ'. -/
theorem Finsupp.total_eq_fintype_total :
(Finsupp.total α M R v).comp (Finsupp.linearEquivFunOnFinite R R α).symm.toLinearMap =
@@ -1805,7 +1805,7 @@ variable {S}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] {S : Type.{u4}} [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{succ u2} (Submodule.{u3, u2} R M _inst_2 _inst_3 _inst_4) (LinearMap.range.{u3, u3, max u1 u3, u2, max (max u1 u3) u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (LinearMap.semilinearMapClass.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (RingHomSurjective.ids.{u3} R _inst_2) (coeFn.{max (succ (max u1 u2)) (succ (max (max u1 u3) u2)), max (succ (max u1 u2)) (succ (max (max u1 u3) u2))} (LinearMap.{u4, u4, max u1 u2, max (max u1 u3) u2} S S _inst_5 _inst_5 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) (fun (_x : LinearMap.{u4, u4, max u1 u2, max (max u1 u3) u2} S S _inst_5 _inst_5 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) => (α -> M) -> (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4)) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, max (max u1 u3) u2} S S (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)) (Submodule.span.{u3, u2} R M _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u1} M α v))
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u4}} (R : Type.{u3}) [_inst_1 : Fintype.{u2} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u3, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u1, u4} R S M (SMulZeroClass.toSMul.{u3, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u4} R M (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u4} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u3, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{succ u4} (Submodule.{u3, u4} R M _inst_2 _inst_3 _inst_4) (LinearMap.range.{u3, u3, max u2 u3, u4, max (max u2 u4) u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) v) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (RingHomSurjective.ids.{u3} R _inst_2) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearMap.{u1, u1, max u2 u4, max u4 u2 u3} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u2, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14077 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.module.{u2, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14077 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u2 u3, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u2, max (max u3 u4) u2} S S (α -> M) (LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u2, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.module.{u2, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14077 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u2 u3, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u2, u4, u3, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)) (Submodule.span.{u3, u4} R M _inst_2 _inst_3 _inst_4 (Set.range.{u4, succ u2} M α v))
+ forall {α : Type.{u2}} {M : Type.{u4}} (R : Type.{u3}) [_inst_1 : Fintype.{u2} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u3, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u1, u4} R S M (SMulZeroClass.toSMul.{u3, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u4} R M (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u4} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u3, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{succ u4} (Submodule.{u3, u4} R M _inst_2 _inst_3 _inst_4) (LinearMap.range.{u3, u3, max u2 u3, u4, max (max u2 u4) u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) v) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (RingHomSurjective.ids.{u3} R _inst_2) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearMap.{u1, u1, max u2 u4, max u4 u2 u3} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u2, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14128 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun 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NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u2, max (max u3 u4) u2} S S (α -> M) (LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u2, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.module.{u2, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14128 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u2 u3, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14140 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u2, u4, u3, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)) (Submodule.span.{u3, u4} R M _inst_2 _inst_3 _inst_4 (Set.range.{u4, succ u2} M α v))
Case conversion may be inaccurate. Consider using '#align fintype.range_total Fintype.range_totalₓ'. -/
@[simp]
theorem Fintype.range_total : (Fintype.total R S v).range = Submodule.span R (Set.range v) := by
@@ -2055,7 +2055,7 @@ theorem splittingOfFinsuppSurjective_injective (f : M →ₗ[R] α →₀ R) (s
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3)
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16678 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u1) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16678 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16678 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16678 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16693 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) _inst_3)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16729 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u1) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16729 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16729 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16729 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16744 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) _inst_3)
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective LinearMap.splittingOfFunOnFintypeSurjectiveₓ'. -/
-- See also `linear_map.splitting_of_finsupp_surjective`
/-- A surjective linear map to functions on a finite type has a splitting. -/
@@ -2069,7 +2069,7 @@ def splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R) (s
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Eq.{succ (max u3 u1)} (LinearMap.{u1, u1, max u3 u1, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (LinearMap.comp.{u1, u1, u1, max u3 u1, u2, max u3 u1} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomCompTriple.right_ids.{u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u1, max u3 u1} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16761 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16761 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16761 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16761 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Eq.{max (succ u2) (succ u3)} (LinearMap.{u2, u2, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16693 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16761 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.comp.{u2, u2, u2, max u2 u3, u1, max u2 u3} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16693 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16761 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u2, max u2 u3} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16693 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16812 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16812 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16812 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16812 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Eq.{max (succ u2) (succ u3)} (LinearMap.{u2, u2, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16744 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16812 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.comp.{u2, u2, u2, max u2 u3, u1, max u2 u3} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16744 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16812 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u2, max u2 u3} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16744 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)))
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective_splits LinearMap.splittingOfFunOnFintypeSurjective_splitsₓ'. -/
theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : f.comp (splittingOfFunOnFintypeSurjective f s) = LinearMap.id :=
@@ -2085,7 +2085,7 @@ theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R]
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Function.LeftInverse.{max (succ u3) (succ u1), succ u2} (α -> R) M (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f) (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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but is expected to have type
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16693 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16693 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => 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+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16944 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), 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Case conversion may be inaccurate. Consider using '#align linear_map.left_inverse_splitting_of_fun_on_fintype_surjective LinearMap.leftInverse_splittingOfFunOnFintypeSurjectiveₓ'. -/
theorem leftInverse_splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : LeftInverse f (splittingOfFunOnFintypeSurjective f s) := fun g =>
@@ -2096,7 +2096,7 @@ theorem leftInverse_splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Function.Injective.{max (succ u3) (succ u1), succ u2} (α -> R) M (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) (fun (_x : LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) => (α -> R) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, u2} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16952 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16952 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16952 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16952 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Function.Injective.{max (succ u2) (succ u3), succ u1} (α -> R) M (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16693 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16693 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16693 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17003 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17003 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17003 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.17003 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Function.Injective.{max (succ u2) (succ u3), succ u1} (α -> R) M (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16744 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16744 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16744 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective_injective LinearMap.splittingOfFunOnFintypeSurjective_injectiveₓ'. -/
theorem splittingOfFunOnFintypeSurjective_injective [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : Injective (splittingOfFunOnFintypeSurjective f s) :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/2196ab363eb097c008d4497125e0dde23fb36db2
@@ -1749,7 +1749,7 @@ variable {S}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] {S : Type.{u4}} [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (f : α -> R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R 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(Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) f) (Finset.sum.{u2, u1} M α _inst_3 (Finset.univ.{u1} α _inst_1) (fun (i : α) => SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (f i) (v i)))
but is expected to have type
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(MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (f : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) f) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R 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NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u3, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14081 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14081 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14081 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) f) (Finset.sum.{u4, u3} M α _inst_3 (Finset.univ.{u3} α _inst_1) (fun (i : α) => HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) (f i) (v i)))
+ forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (f : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) f) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) v) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearMap.{u1, u1, max u3 u4, max u4 u3 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u3, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14077 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14077 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14077 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) f) (Finset.sum.{u4, u3} M α _inst_3 (Finset.univ.{u3} α _inst_1) (fun (i : α) => HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) (f i) (v i)))
Case conversion may be inaccurate. Consider using '#align fintype.total_apply Fintype.total_applyₓ'. -/
theorem Fintype.total_apply (f) : Fintype.total R S v f = ∑ i, f i • v i :=
rfl
@@ -1759,7 +1759,7 @@ theorem Fintype.total_apply (f) : Fintype.total R S v f = ∑ i, f i • v i :=
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] {S : Type.{u4}} [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (i : α) (r : R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R 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(Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) (Pi.single.{u1, u3} α (fun (ᾰ : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u1} α a b)) (fun (i : α) => MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) i r)) (SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) r (v i))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (i : α) (r : R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) (Pi.single.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} 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_inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14081 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) (Pi.single.{u3, u2} α (fun (ᾰ : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) r (v i))
+ forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (i : α) (r : R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) (Pi.single.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) v) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearMap.{u1, u1, max u3 u4, max u4 u3 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14077 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) (Pi.single.{u3, u2} α (fun (ᾰ : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) r (v i))
Case conversion may be inaccurate. Consider using '#align fintype.total_apply_single Fintype.total_apply_singleₓ'. -/
@[simp]
theorem Fintype.total_apply_single (i : α) (r : R) :
@@ -1775,7 +1775,7 @@ variable (S)
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] (S : Type.{u4}) [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (x : α -> R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R 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u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Finsupp.total.{u1, u2, u3} α M R _inst_2 _inst_3 _inst_4 v) (coeFn.{succ (max u1 u3), succ (max u1 u3)} (LinearEquiv.{u3, u3, max u1 u3, max u1 u3} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHomInvPair.ids.{u3} R _inst_2) (RingHomInvPair.ids.{u3} R _inst_2) (α -> R) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R 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(Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) x)
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (x : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) => M) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (α -> R) (fun (a : α -> R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> R) => Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) a) (SMulHomClass.toFunLike.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R 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(Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (α -> R) (AddMonoid.toZero.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (α -> R) (AddMonoid.toAddZeroClass.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (α -> R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u3 u2, max u3 u2, max u3 u2} R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u3 u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2)))))) (LinearEquiv.symm.{u2, u2, max u3 u2, max u3 u2} R R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (α -> R) _inst_2 _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (Finsupp.linearEquivFunOnFinite.{u2, u2, u3} R R α (Finite.of_fintype.{u3} α _inst_1) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R 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(Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14081 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14081 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) x)
+ forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (x : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) => M) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (α -> R) (fun (a : α -> R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> R) => Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) a) (SMulHomClass.toFunLike.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (α -> R) (AddMonoid.toZero.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (α -> R) (AddMonoid.toAddZeroClass.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (α -> R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u3 u2, max u3 u2, max u3 u2} R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u3 u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R 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Case conversion may be inaccurate. Consider using '#align finsupp.total_eq_fintype_total_apply Finsupp.total_eq_fintype_total_applyₓ'. -/
theorem Finsupp.total_eq_fintype_total_apply (x : α → R) :
Finsupp.total α M R v ((Finsupp.linearEquivFunOnFinite R R α).symm x) = Fintype.total R S v x :=
@@ -1791,7 +1791,7 @@ theorem Finsupp.total_eq_fintype_total_apply (x : α → R) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] (S : Type.{u4}) [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (LinearMap.comp.{u3, u3, u3, max u1 u3, max u1 u3, u2} R R R (α -> R) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))) M _inst_2 _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHomCompTriple.right_ids.{u3, u3} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Finsupp.total.{u1, u2, u3} α M R _inst_2 _inst_3 _inst_4 v) (LinearEquiv.toLinearMap.{u3, u3, max u1 u3, max u1 u3} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHomInvPair.ids.{u3} R _inst_2) (RingHomInvPair.ids.{u3} R _inst_2) (α -> R) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))))) (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) (LinearEquiv.symm.{u3, u3, max u1 u3, max u1 u3} R R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))))) (α -> R) _inst_2 _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHomInvPair.ids.{u3} R _inst_2) (RingHomInvPair.ids.{u3} R _inst_2) (Finsupp.linearEquivFunOnFinite.{u3, u3, u1} R R α (Finite.of_fintype.{u1} α _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) _inst_2 (Semiring.toModule.{u3} R _inst_2))))) (coeFn.{max (succ (max u1 u2)) (succ (max (max u1 u3) u2)), max (succ (max u1 u2)) (succ (max (max u1 u3) u2))} (LinearMap.{u4, u4, max u1 u2, max (max u1 u3) u2} S S _inst_5 _inst_5 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4)) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, max (max u1 u3) u2} S S (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)
but is expected to have type
- forall {α : Type.{u4}} {M : Type.{u3}} (R : Type.{u2}) [_inst_1 : Fintype.{u4} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u3} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u3} R S M (SMulZeroClass.toSMul.{u2, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u2, u3} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u3} S M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u1, u3} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (LinearMap.comp.{u2, u2, u2, max u4 u2, max u4 u2, u3} R R R (α -> R) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) M _inst_2 _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomCompTriple.ids.{u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Finsupp.total.{u4, u3, u2} α M R _inst_2 _inst_3 _inst_4 v) (LinearEquiv.toLinearMap.{u2, u2, max u4 u2, max u4 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u4, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (LinearEquiv.symm.{u2, u2, max u4 u2, max u4 u2} R R (Finsupp.{u4, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (α -> R) _inst_2 _inst_2 (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (Finsupp.linearEquivFunOnFinite.{u2, u2, u4} R R α (Finite.of_fintype.{u4} α _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) _inst_2 (Semiring.toModule.{u2} R _inst_2))))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), max (max (succ u2) (succ u3)) (succ u4)} (LinearMap.{u1, u1, max u4 u3, max u3 u4 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u4, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14081 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u4 u2, u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u4, u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14081 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u4 u2, u3} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u4, max (max u2 u3) u4} S S (α -> M) (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u4, u3} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u4 u2, u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u4, u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14081 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u4 u2, u3} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u4, u3, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)
+ forall {α : Type.{u4}} {M : Type.{u3}} (R : Type.{u2}) [_inst_1 : Fintype.{u4} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u3} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u3} R S M (SMulZeroClass.toSMul.{u2, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u2, u3} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u3} S M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u1, u3} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (LinearMap.comp.{u2, u2, u2, max u4 u2, max u4 u2, u3} R R R (α -> R) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) M _inst_2 _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomCompTriple.ids.{u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Finsupp.total.{u4, u3, u2} α M R _inst_2 _inst_3 _inst_4 v) (LinearEquiv.toLinearMap.{u2, u2, max u4 u2, max u4 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u4, u2} α R (AddMonoid.toZero.{u2} R 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_inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u4, u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14077 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u4 u2, u3} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u4, u3, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)
Case conversion may be inaccurate. Consider using '#align finsupp.total_eq_fintype_total Finsupp.total_eq_fintype_totalₓ'. -/
theorem Finsupp.total_eq_fintype_total :
(Finsupp.total α M R v).comp (Finsupp.linearEquivFunOnFinite R R α).symm.toLinearMap =
@@ -1805,7 +1805,7 @@ variable {S}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] {S : Type.{u4}} [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{succ u2} (Submodule.{u3, u2} R M _inst_2 _inst_3 _inst_4) (LinearMap.range.{u3, u3, max u1 u3, u2, max (max u1 u3) u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (LinearMap.semilinearMapClass.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (RingHomSurjective.ids.{u3} R _inst_2) (coeFn.{max (succ (max u1 u2)) (succ (max (max u1 u3) u2)), max (succ (max u1 u2)) (succ (max (max u1 u3) u2))} (LinearMap.{u4, u4, max u1 u2, max (max u1 u3) u2} S S _inst_5 _inst_5 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) (fun (_x : LinearMap.{u4, u4, max u1 u2, max (max u1 u3) u2} S S _inst_5 _inst_5 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) => (α -> M) -> (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4)) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, max (max u1 u3) u2} S S (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)) (Submodule.span.{u3, u2} R M _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u1} M α v))
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u4}} (R : Type.{u3}) [_inst_1 : Fintype.{u2} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u3, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u1, u4} R S M (SMulZeroClass.toSMul.{u3, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u4} R M (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u4} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u3, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{succ u4} (Submodule.{u3, u4} R M _inst_2 _inst_3 _inst_4) (LinearMap.range.{u3, u3, max u2 u3, u4, max (max u2 u4) u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) v) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (RingHomSurjective.ids.{u3} R _inst_2) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearMap.{u1, u1, max u2 u4, max u4 u2 u3} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u2, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14081 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.module.{u2, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14081 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u2 u3, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) (fun (i : α) => 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(Pi.module.{u2, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14081 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u2 u3, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u2, u4, u3, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)) (Submodule.span.{u3, u4} R M _inst_2 _inst_3 _inst_4 (Set.range.{u4, succ u2} M α v))
+ forall {α : Type.{u2}} {M : Type.{u4}} (R : Type.{u3}) [_inst_1 : Fintype.{u2} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u3, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u1, u4} R S M (SMulZeroClass.toSMul.{u3, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u4} R M (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u4} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u3, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{succ u4} (Submodule.{u3, u4} R M _inst_2 _inst_3 _inst_4) (LinearMap.range.{u3, u3, max u2 u3, u4, max (max u2 u4) u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) v) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (RingHomSurjective.ids.{u3} R _inst_2) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearMap.{u1, u1, max u2 u4, max u4 u2 u3} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u2, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14077 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.module.{u2, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14077 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u2 u3, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u2, max (max u3 u4) u2} S S (α -> M) (LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u2, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.module.{u2, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14077 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u2 u3, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14089 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u2, u4, u3, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)) (Submodule.span.{u3, u4} R M _inst_2 _inst_3 _inst_4 (Set.range.{u4, succ u2} M α v))
Case conversion may be inaccurate. Consider using '#align fintype.range_total Fintype.range_totalₓ'. -/
@[simp]
theorem Fintype.range_total : (Fintype.total R S v).range = Submodule.span R (Set.range v) := by
@@ -2055,7 +2055,7 @@ theorem splittingOfFinsuppSurjective_injective (f : M →ₗ[R] α →₀ R) (s
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3)
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16682 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u1) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16682 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16682 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16682 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16697 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) _inst_3)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16678 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u1) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16678 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16678 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16678 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16693 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) _inst_3)
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective LinearMap.splittingOfFunOnFintypeSurjectiveₓ'. -/
-- See also `linear_map.splitting_of_finsupp_surjective`
/-- A surjective linear map to functions on a finite type has a splitting. -/
@@ -2069,7 +2069,7 @@ def splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R) (s
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Eq.{succ (max u3 u1)} (LinearMap.{u1, u1, max u3 u1, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (LinearMap.comp.{u1, u1, u1, max u3 u1, u2, max u3 u1} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomCompTriple.right_ids.{u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u1, max u3 u1} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16765 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16765 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16765 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16765 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Eq.{max (succ u2) (succ u3)} (LinearMap.{u2, u2, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16697 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16765 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.comp.{u2, u2, u2, max u2 u3, u1, max u2 u3} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16697 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16765 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u2, max u2 u3} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16697 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16761 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16761 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16761 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16761 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Eq.{max (succ u2) (succ u3)} (LinearMap.{u2, u2, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16693 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16761 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.comp.{u2, u2, u2, max u2 u3, u1, max u2 u3} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16693 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16761 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u2, max u2 u3} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16693 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)))
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective_splits LinearMap.splittingOfFunOnFintypeSurjective_splitsₓ'. -/
theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : f.comp (splittingOfFunOnFintypeSurjective f s) = LinearMap.id :=
@@ -2085,7 +2085,7 @@ theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R]
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Function.LeftInverse.{max (succ u3) (succ u1), succ u2} (α -> R) M (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f) (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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but is expected to have type
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16697 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16697 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => 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+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16893 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), 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Case conversion may be inaccurate. Consider using '#align linear_map.left_inverse_splitting_of_fun_on_fintype_surjective LinearMap.leftInverse_splittingOfFunOnFintypeSurjectiveₓ'. -/
theorem leftInverse_splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : LeftInverse f (splittingOfFunOnFintypeSurjective f s) := fun g =>
@@ -2096,7 +2096,7 @@ theorem leftInverse_splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Function.Injective.{max (succ u3) (succ u1), succ u2} (α -> R) M (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) (fun (_x : LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) => (α -> R) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, u2} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16956 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16956 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16956 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16956 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Function.Injective.{max (succ u2) (succ u3), succ u1} (α -> R) M (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16697 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16697 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16697 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16952 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16952 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16952 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16952 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Function.Injective.{max (succ u2) (succ u3), succ u1} (α -> R) M (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16693 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16693 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16693 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective_injective LinearMap.splittingOfFunOnFintypeSurjective_injectiveₓ'. -/
theorem splittingOfFunOnFintypeSurjective_injective [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : Injective (splittingOfFunOnFintypeSurjective f s) :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212
@@ -91,7 +91,7 @@ def lsingle (a : α) : M →ₗ[R] α →₀ M :=
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} [_inst_1 : Semiring.{u4} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] {{φ : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6}} {{ψ : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6}}, (forall (a : α) (b : M), Eq.{succ u3} N (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (fun (_x : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) => (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) -> N) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) φ (Finsupp.single.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) a b)) (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (fun (_x : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) => (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) -> N) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) ψ (Finsupp.single.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) a b))) -> (Eq.{max (succ (max u1 u2)) (succ u3)} (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) φ ψ)
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u3}} {N : Type.{u1}} {R : Type.{u4}} [_inst_1 : Semiring.{u4} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u4, u3} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : Module.{u4, u1} R N _inst_1 _inst_5] {{φ : LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6}} {{ψ : LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6}}, (forall (a : α) (b : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => N) (Finsupp.single.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) a b)) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u3), succ u1} (LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (fun (_x : Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u2 u3, u1} R R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) φ (Finsupp.single.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) a b)) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u3), succ u1} (LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (fun (_x : Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u2 u3, u1} R R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) ψ (Finsupp.single.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) a b))) -> (Eq.{max (max (succ u2) (succ u3)) (succ u1)} (LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) φ ψ)
+ forall {α : Type.{u2}} {M : Type.{u3}} {N : Type.{u1}} {R : Type.{u4}} [_inst_1 : Semiring.{u4} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u4, u3} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : Module.{u4, u1} R N _inst_1 _inst_5] {{φ : LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6}} {{ψ : LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6}}, (forall (a : α) (b : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => N) (Finsupp.single.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) a b)) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u3), succ u1} (LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (fun (_x : Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u2 u3, u1} R R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) φ (Finsupp.single.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) a b)) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u3), succ u1} (LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (fun (_x : Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u2 u3, u1} R R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) ψ (Finsupp.single.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) a b))) -> (Eq.{max (max (succ u2) (succ u3)) (succ u1)} (LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) φ ψ)
Case conversion may be inaccurate. Consider using '#align finsupp.lhom_ext Finsupp.lhom_extₓ'. -/
/-- Two `R`-linear maps from `finsupp X M` which agree on each `single x y` agree everywhere. -/
theorem lhom_ext ⦃φ ψ : (α →₀ M) →ₗ[R] N⦄ (h : ∀ a b, φ (single a b) = ψ (single a b)) : φ = ψ :=
@@ -130,7 +130,7 @@ def lapply (a : α) : (α →₀ M) →ₗ[R] M :=
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], LinearMap.{u3, u3, max u1 u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (α -> M) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Pi.Function.module.{u1, u3, u2} α R M _inst_1 _inst_3 _inst_4)
but is expected to have type
- forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], LinearMap.{u3, u3, max u2 u1, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (α -> M) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Pi.module.{u1, u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.497 : α) => M) R _inst_1 (fun (i : α) => _inst_3) (fun (i : α) => _inst_4))
+ forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], LinearMap.{u3, u3, max u2 u1, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (α -> M) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Pi.module.{u1, u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.499 : α) => M) R _inst_1 (fun (i : α) => _inst_3) (fun (i : α) => _inst_4))
Case conversion may be inaccurate. Consider using '#align finsupp.lcoe_fun Finsupp.lcoeFunₓ'. -/
/-- Forget that a function is finitely supported.
@@ -168,7 +168,7 @@ def lsubtypeDomain : (α →₀ M) →ₗ[R] s →₀ M
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α) (f : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))), Eq.{max (succ u1) (succ u2)} (Finsupp.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u3, u3, max u1 u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) M R _inst_1 _inst_3 _inst_4)) (fun (_x : LinearMap.{u3, u3, max u1 u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) M R _inst_1 _inst_3 _inst_4)) => (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) -> (Finsupp.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))))) (LinearMap.hasCoeToFun.{u3, u3, max u1 u2, max u1 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lsubtypeDomain.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s) f) (Finsupp.subtypeDomain.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) f)
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (f : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Finsupp.{u3, u2} (Set.Elem.{u3} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) f) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearMap.{u1, u1, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} (Set.Elem.{u3} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} (Set.Elem.{u3} α s) M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} (Set.Elem.{u3} α s) M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (_x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Finsupp.{u3, u2} (Set.Elem.{u3} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u2, max u3 u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} (Set.Elem.{u3} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} (Set.Elem.{u3} α s) M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} (Set.Elem.{u3} α s) M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lsubtypeDomain.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) f) (Finsupp.subtypeDomain.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (fun (x : α) => Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) x s) f)
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (f : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Finsupp.{u3, u2} (Set.Elem.{u3} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) f) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearMap.{u1, u1, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} (Set.Elem.{u3} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} (Set.Elem.{u3} α s) M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} (Set.Elem.{u3} α s) M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (_x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Finsupp.{u3, u2} (Set.Elem.{u3} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u2, max u3 u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} (Set.Elem.{u3} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} (Set.Elem.{u3} α s) M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} (Set.Elem.{u3} α s) M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lsubtypeDomain.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) f) (Finsupp.subtypeDomain.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (fun (x : α) => Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) x s) f)
Case conversion may be inaccurate. Consider using '#align finsupp.lsubtype_domain_apply Finsupp.lsubtypeDomain_applyₓ'. -/
theorem lsubtypeDomain_apply (f : α →₀ M) :
(lsubtypeDomain s : (α →₀ M) →ₗ[R] s →₀ M) f = subtypeDomain (fun x => x ∈ s) f :=
@@ -181,7 +181,7 @@ end LsubtypeDomain
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (a : α) (b : M), Eq.{max (succ u1) (succ u2)} (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (fun (_x : LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) => M -> (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))))) (LinearMap.hasCoeToFun.{u3, u3, u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lsingle.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a) b) (Finsupp.single.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) a b)
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (a : α) (b : M), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) b) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a) b) (Finsupp.single.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) a b)
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (a : α) (b : M), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) b) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a) b) (Finsupp.single.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) a b)
Case conversion may be inaccurate. Consider using '#align finsupp.lsingle_apply Finsupp.lsingle_applyₓ'. -/
@[simp]
theorem lsingle_apply (a : α) (b : M) : (lsingle a : M →ₗ[R] α →₀ M) b = single a b :=
@@ -192,7 +192,7 @@ theorem lsingle_apply (a : α) (b : M) : (lsingle a : M →ₗ[R] α →₀ M) b
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (a : α) (f : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))), Eq.{succ u2} M (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (LinearMap.{u3, u3, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4) => (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u2, u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lapply.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a) f) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (fun (_x : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) => α -> M) (Finsupp.coeFun.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) f a)
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (a : α) (f : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => M) f) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), succ u2} (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (_x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u2, u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lapply.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a) f) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) α (fun (_x : α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) _x) (Finsupp.funLike.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) f a)
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (a : α) (f : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => M) f) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), succ u2} (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (_x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u2, u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lapply.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a) f) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) α (fun (_x : α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) _x) (Finsupp.funLike.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) f a)
Case conversion may be inaccurate. Consider using '#align finsupp.lapply_apply Finsupp.lapply_applyₓ'. -/
@[simp]
theorem lapply_apply (a : α) (f : α →₀ M) : (lapply a : (α →₀ M) →ₗ[R] M) f = f a :=
@@ -399,7 +399,7 @@ section
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α) (l : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))), Eq.{max (succ u1) (succ u2)} (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) ((fun (a : Type.{max u1 u2}) (b : Sort.{max (succ u1) (succ u2)}) [self : HasLiftT.{succ (max u1 u2), max (succ u1) (succ u2)} a b] => self.0) (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (HasLiftT.mk.{succ (max u1 u2), max (succ u1) (succ u2)} (coeSort.{succ (max u1 u2), succ (succ (max 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(Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.restrictDom.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) l)) (Finsupp.filter.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (fun (_x : α) => Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) _x s) l)
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (l : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))), Eq.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Subtype.val.{succ (max u3 u2)} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u3 u2, max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Set.{max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Set.instMembershipSet.{max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) x (SetLike.coe.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s))) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearMap.{u1, u1, max u2 u3, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Subtype.{succ (max u3 u2)} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u3 u2, max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u1, 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(AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s))) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (_x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Subtype.{succ (max u3 u2)} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u3 u2, max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) x (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u2, max u3 u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M 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_inst_3))) (Submodule.instSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) x (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.restrictDom.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) l)) (Finsupp.filter.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (fun (_x : α) => Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) _x s) l)
Case conversion may be inaccurate. Consider using '#align finsupp.restrict_dom_apply Finsupp.restrictDom_applyₓ'. -/
@[simp]
theorem restrictDom_apply (s : Set α) (l : α →₀ M) :
@@ -576,7 +576,7 @@ variable (S) [Module S N] [SMulCommClass R S N]
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toHasSmul.{u4, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u4, u3} R N (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u5, u3} S N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u5, u3} S N (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))], LinearEquiv.{u5, u5, max u1 u2 u3, max (max u1 u2) u3} S S _inst_2 _inst_2 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2) (α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u1, max u2 u3} α (fun (ᾰ : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.Function.module.{u1, u5, max u2 u3} α S (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.module.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.module.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)
but is expected to have type
- forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toSMul.{u4, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u4, u3} R N (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u5, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} S N (MonoidWithZero.toZero.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))], LinearEquiv.{u5, u5, max (max u1 u2) u3, max u3 u2 u1} S S _inst_2 _inst_2 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2) (α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u4, u4, max u2 u1, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u1, max u2 u3} α (fun (ᾰ : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.module.{u1, max u2 u3, u5} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)
+ forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toSMul.{u4, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u4, u3} R N (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u5, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} S N (MonoidWithZero.toZero.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))], LinearEquiv.{u5, u5, max (max u1 u2) u3, max u3 u2 u1} S S _inst_2 _inst_2 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2) (α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u4, u4, max u2 u1, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u1, max u2 u3} α (fun (ᾰ : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.module.{u1, max u2 u3, u5} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)
Case conversion may be inaccurate. Consider using '#align finsupp.lsum Finsupp.lsumₓ'. -/
/-- Lift a family of linear maps `M →ₗ[R] N` indexed by `x : α` to a linear map from `α →₀ M` to
`N` using `finsupp.sum`. This is an upgraded version of `finsupp.lift_add_hom`.
@@ -608,7 +608,7 @@ def lsum : (α → M →ₗ[R] N) ≃ₗ[S] (α →₀ M) →ₗ[R] N
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toHasSmul.{u4, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u4, u3} R N (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u5, u3} S N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u5, u3} S N (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)), Eq.{max (max (succ u1) (succ u2)) (succ u3)} ((fun (_x : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) => (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) -> N) (coeFn.{max (succ (max u1 u2 u3)) (succ (max (max u1 u2) u3)), max (succ (max u1 u2 u3)) (succ (max (max u1 u2) u3))} (LinearEquiv.{u5, u5, max u1 u2 u3, max (max u1 u2) u3} S S _inst_2 _inst_2 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S 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=> LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.Function.module.{u1, u5, max u2 u3} α S (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.module.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.module.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2)) (Finsupp.lsum.{u1, u2, u3, u4, u5} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f)) (fun (d : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) => Finsupp.sum.{u1, u2, u3} α M N (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_5 d (fun (i : α) => coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (_x : LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) => M -> N) (LinearMap.hasCoeToFun.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (f i)))
but is expected to have type
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(AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)), Eq.{max (max (succ u2) (succ u4)) (succ u3)} (forall (a : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) a) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) 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(LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R 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_inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M 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(LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2} S S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f)) (fun (d : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => Finsupp.sum.{u2, u4, u3} α M ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) d) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) _inst_5 d (fun (i : α) => FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f i)))
+ forall {α : Type.{u2}} {M : Type.{u4}} {N : Type.{u3}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u3} R S N (SMulZeroClass.toSMul.{u5, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)), Eq.{max (max (succ u2) (succ u4)) (succ u3)} (forall (a : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) a) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) f) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (fun (_x : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (fun (_x : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _x) (SMulHomClass.toFunLike.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M 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(RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f)) (fun (d : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => Finsupp.sum.{u2, u4, u3} α M ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) d) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) _inst_5 d (fun (i : α) => FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f i)))
Case conversion may be inaccurate. Consider using '#align finsupp.coe_lsum Finsupp.coe_lsumₓ'. -/
@[simp]
theorem coe_lsum (f : α → M →ₗ[R] N) : (lsum S f : (α →₀ M) → N) = fun d => d.Sum fun i => f i :=
@@ -619,7 +619,7 @@ theorem coe_lsum (f : α → M →ₗ[R] N) : (lsum S f : (α →₀ M) → N) =
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toHasSmul.{u4, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u4, u3} R N (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u5, u3} S N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u5, u3} S N (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (l : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))), Eq.{succ u3} N (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (fun (_x : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 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_inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u1, max u2 u3} α (fun (ᾰ : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.Function.module.{u1, u5, max u2 u3} α S (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.module.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.module.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2)) (Finsupp.lsum.{u1, u2, u3, u4, u5} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f) l) (Finsupp.sum.{u1, u2, u3} α M N (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_5 l (fun (b : α) => coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (_x : LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) => M -> N) (LinearMap.hasCoeToFun.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (f b)))
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u4}} {N : Type.{u3}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u3} R S N (SMulZeroClass.toSMul.{u5, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (l : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) l) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), succ u3} ((fun 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_inst_2 _inst_9 _inst_10)) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (fun (_x : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _x) (SMulHomClass.toFunLike.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} 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_inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R 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_inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M 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(AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2} S S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f) l) (Finsupp.sum.{u2, u4, u3} α M N (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) _inst_5 l (fun (b : α) => FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f b)))
+ forall {α : Type.{u2}} {M : Type.{u4}} {N : Type.{u3}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u3} R S N (SMulZeroClass.toSMul.{u5, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (l : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) l) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) f) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (fun (_x : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (fun (_x : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _x) (SMulHomClass.toFunLike.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} 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_inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R 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(RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f) l) (Finsupp.sum.{u2, u4, u3} α M N (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) _inst_5 l (fun (b : α) => FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f b)))
Case conversion may be inaccurate. Consider using '#align finsupp.lsum_apply Finsupp.lsum_applyₓ'. -/
theorem lsum_apply (f : α → M →ₗ[R] N) (l : α →₀ M) : Finsupp.lsum S f l = l.Sum fun b => f b :=
rfl
@@ -629,7 +629,7 @@ theorem lsum_apply (f : α → M →ₗ[R] N) (l : α →₀ M) : Finsupp.lsum S
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toHasSmul.{u4, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u4, u3} R N (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u5, u3} S N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u5, u3} S N (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N 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(AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (i : α) (m : M), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) (Finsupp.single.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) i m)) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), succ u3} 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_inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => 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(Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 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(AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 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R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2} S S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f) (Finsupp.single.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) i m)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f i) m)
+ forall {α : Type.{u2}} {M : Type.{u4}} {N : Type.{u3}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u3} R S N (SMulZeroClass.toSMul.{u5, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (i : α) (m : M), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) (Finsupp.single.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) i m)) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) f) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (fun (_x : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (fun (_x : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _x) (SMulHomClass.toFunLike.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M 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(RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M 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u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) 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_inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2} S S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f) (Finsupp.single.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) i m)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f i) m)
Case conversion may be inaccurate. Consider using '#align finsupp.lsum_single Finsupp.lsum_singleₓ'. -/
theorem lsum_single (f : α → M →ₗ[R] N) (i : α) (m : M) :
Finsupp.lsum S f (Finsupp.single i m) = f i m :=
@@ -640,7 +640,7 @@ theorem lsum_single (f : α → M →ₗ[R] N) (i : α) (m : M) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toHasSmul.{u4, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u4, u3} R N (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u5, u3} S N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u5, u3} S N (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))] (f : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (x : α), Eq.{max (succ u2) (succ u3)} (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (coeFn.{max (succ (max (max u1 u2) u3)) (succ (max u1 u2 u3)), max (succ (max (max u1 u2) u3)) (succ (max u1 u2 u3))} (LinearEquiv.{u5, u5, max (max u1 u2) u3, max u1 u2 u3} S S _inst_2 _inst_2 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2) (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M 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(AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.Function.module.{u1, u5, max u2 u3} α S (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.module.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.module.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2) (Finsupp.lsum.{u1, u2, u3, u4, u5} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10)) f x) (LinearMap.comp.{u4, u4, u4, u2, max u1 u2, u3} R R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 _inst_4 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomCompTriple.right_ids.{u4, u4} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) f (Finsupp.lsingle.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4 x))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u4}} {N : Type.{u2}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : Module.{u5, u2} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u2} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u2} R S N (SMulZeroClass.toSMul.{u5, u2} R N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u2} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u2} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (Module.toMulActionWithZero.{u5, u2} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u2} S N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u2} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u2} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (Module.toMulActionWithZero.{u1, u2} S N _inst_2 _inst_5 _inst_9))))] (f : LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (x : α), Eq.{max (succ u4) (succ u2)} (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (max (succ u2) (succ u4)) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (fun (_x : LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) => α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _x) (SMulHomClass.toFunLike.{max (max u2 u4) u3, u1, max (max u2 u4) u3, max (max u2 u4) u3} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (SMulZeroClass.toSMul.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (SMulZeroClass.toSMul.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u4) u3, u1, max (max u2 u4) u3, max (max u2 u4) u3} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u2 u4) u3, max (max u2 u4) u3, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3, max (max u2 u4) u3} S S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) _inst_2 _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (LinearEquiv.symm.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (ᾰ : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (Finsupp.lsum.{u3, u4, u2, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10)) f x) (LinearMap.comp.{u5, u5, u5, u4, max u3 u4, u2} R R R M (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 _inst_4 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHomCompTriple.ids.{u5, u5} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) f (Finsupp.lsingle.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4 x))
+ forall {α : Type.{u3}} {M : Type.{u4}} {N : Type.{u2}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : Module.{u5, u2} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u2} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u2} R S N (SMulZeroClass.toSMul.{u5, u2} R N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u2} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u2} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (Module.toMulActionWithZero.{u5, u2} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u2} S N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u2} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u2} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (Module.toMulActionWithZero.{u1, u2} S N _inst_2 _inst_5 _inst_9))))] (f : LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (x : α), Eq.{max (succ u4) (succ u2)} (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (max (succ u2) (succ u4)) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (fun (_x : LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) => α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _x) (SMulHomClass.toFunLike.{max (max u2 u4) u3, u1, max (max u2 u4) u3, max (max u2 u4) u3} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (SMulZeroClass.toSMul.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (SMulZeroClass.toSMul.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u4) u3, u1, max (max u2 u4) u3, max (max u2 u4) u3} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u2 u4) u3, max (max u2 u4) u3, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R 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_inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M 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(Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4422 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (LinearEquiv.symm.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (ᾰ : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 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(RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (Finsupp.lsum.{u3, u4, u2, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10)) f x) (LinearMap.comp.{u5, u5, u5, u4, max u3 u4, u2} R R R M (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 _inst_4 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHomCompTriple.ids.{u5, u5} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) f (Finsupp.lsingle.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4 x))
Case conversion may be inaccurate. Consider using '#align finsupp.lsum_symm_apply Finsupp.lsum_symm_applyₓ'. -/
theorem lsum_symm_apply (f : (α →₀ M) →ₗ[R] N) (x : α) : (lsum S).symm f x = f.comp (lsingle x) :=
rfl
@@ -670,7 +670,7 @@ noncomputable def lift : (X → M) ≃+ ((X →₀ R) →ₗ[R] M) :=
lean 3 declaration is
forall (M : Type.{u1}) (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u3}) (f : LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (x : X), Eq.{succ u1} M (coeFn.{max (succ (max (max u3 u2) u1)) (succ 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(NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.instAdd.{u3, u1} X (fun (ᾰ : X) => M) (fun (i : X) => AddZeroClass.toHasAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (fun (_x : AddEquiv.{max (max u3 u2) u1, max u3 u1} (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (X -> M) (LinearMap.hasAdd.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.instAdd.{u3, u1} X (fun (ᾰ : X) => M) (fun (i : X) => AddZeroClass.toHasAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) => (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) -> X -> M) (AddEquiv.hasCoeToFun.{max (max u3 u2) u1, max u3 u1} (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (X -> M) (LinearMap.hasAdd.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.instAdd.{u3, u1} X (fun (ᾰ : X) => M) (fun (i : X) => AddZeroClass.toHasAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (AddEquiv.symm.{max u3 u1, max (max u3 u2) u1} (X -> M) (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (ᾰ : X) => M) (fun (i : X) => AddZeroClass.toHasAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.hasAdd.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.lift.{u1, u2, u3} M R _inst_1 _inst_3 _inst_4 X)) f x) (coeFn.{max (succ (max u3 u2)) (succ u1), max (succ (max u3 u2)) (succ u1)} (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) => (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f (Finsupp.single.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) x (OfNat.ofNat.{u2} R 1 (OfNat.mk.{u2} R 1 (One.one.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))))))
but is expected to have type
- forall (M : Type.{u1}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_3] (X : Type.{u2}) (f : LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (x : X), Eq.{succ u1} M (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2)} (AddEquiv.{max (max u1 u3) u2, max u1 u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (LinearMap.instAddLinearMap.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.instAdd.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4916 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => X -> M) _x) (AddHomClass.toFunLike.{max (max u1 u3) u2, max (max u1 u3) u2, max u1 u2} (AddEquiv.{max (max u1 u3) u2, max u1 u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (LinearMap.instAddLinearMap.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.instAdd.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4916 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (AddZeroClass.toAdd.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddMonoid.toAddZeroClass.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (AddZeroClass.toAdd.{max u1 u2} (X -> M) (Pi.addZeroClass.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4916 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (AddMonoidHomClass.toAddHomClass.{max (max u1 u3) u2, max (max u1 u3) u2, max u1 u2} (AddEquiv.{max (max u1 u3) u2, max u1 u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (LinearMap.instAddLinearMap.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.instAdd.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4916 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (AddMonoid.toAddZeroClass.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Pi.addZeroClass.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4916 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddEquivClass.instAddMonoidHomClass.{max (max u1 u3) u2, max (max u1 u3) u2, max u1 u2} (AddEquiv.{max (max u1 u3) u2, max u1 u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (LinearMap.instAddLinearMap.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.instAdd.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4916 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (AddMonoid.toAddZeroClass.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Pi.addZeroClass.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4916 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddEquiv.instAddEquivClassAddEquiv.{max (max u1 u3) u2, max u1 u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (LinearMap.instAddLinearMap.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.instAdd.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4916 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))) (AddEquiv.symm.{max u1 u2, max (max u1 u3) u2} (X -> M) (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lift.{u1, u3, u2} M R _inst_1 _inst_3 _inst_4 X)) f x) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R 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+ forall (M : Type.{u1}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_3] (X : Type.{u2}) (f : LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (x : X), Eq.{succ u1} M (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2)} (AddEquiv.{max (max u1 u3) u2, 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u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (LinearMap.instAddLinearMap.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.instAdd.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4940 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (AddZeroClass.toAdd.{max (max u1 u3) u2} (LinearMap.{u3, 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R 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Case conversion may be inaccurate. Consider using '#align finsupp.lift_symm_apply Finsupp.lift_symm_applyₓ'. -/
@[simp]
theorem lift_symm_apply (f) (x) : ((lift M R X).symm f) x = f (single x 1) :=
@@ -681,7 +681,7 @@ theorem lift_symm_apply (f) (x) : ((lift M R X).symm f) x = f (single x 1) :=
lean 3 declaration is
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(Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) 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(NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) => (X -> M) -> (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R 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(Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (ᾰ : X) => M) (fun (i : X) => AddZeroClass.toHasAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.hasAdd.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.lift.{u1, u2, u3} M R _inst_1 _inst_3 _inst_4 X) f) g) (Finsupp.sum.{u3, u2, u1} X R M (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 g (fun (x : X) (r : R) => SMul.smul.{u2, u1} R M (SMulZeroClass.toHasSmul.{u2, u1} R M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u1} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4)))) r (f x)))
but is expected to have type
- forall (M : Type.{u1}) (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u3}) (f : X -> M) (g : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) g) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : X -> M) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) f) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (max (succ u1) (succ u2)) (succ u3)} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4916 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (fun (_x : X -> M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : X -> M) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) _x) (AddHomClass.toFunLike.{max (max u1 u2) u3, max u1 u3, max (max u1 u2) u3} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4916 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddZeroClass.toAdd.{max u1 u3} (X -> M) (Pi.addZeroClass.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4916 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (AddZeroClass.toAdd.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (AddMonoidHomClass.toAddHomClass.{max (max u1 u2) u3, max u1 u3, max (max u1 u2) u3} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4916 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.addZeroClass.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4916 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddEquivClass.instAddMonoidHomClass.{max (max u1 u2) u3, max u1 u3, max (max u1 u2) u3} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4916 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.addZeroClass.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4916 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddEquiv.instAddEquivClassAddEquiv.{max u1 u3, max (max u1 u2) u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4916 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (Finsupp.lift.{u1, u2, u3} M R _inst_1 _inst_3 _inst_4 X) f) g) (Finsupp.sum.{u3, u2, u1} X R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) _inst_3 g (fun (x : X) (r : R) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4))))) r (f x)))
+ forall (M : Type.{u1}) (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u3}) (f : X -> M) (g : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) g) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : X -> M) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) f) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (max (succ u1) (succ u2)) (succ u3)} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4940 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (fun (_x : X -> M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : X -> M) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) _x) (AddHomClass.toFunLike.{max (max u1 u2) u3, max u1 u3, max (max u1 u2) u3} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4940 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddZeroClass.toAdd.{max u1 u3} (X -> M) (Pi.addZeroClass.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4940 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (AddZeroClass.toAdd.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (AddMonoidHomClass.toAddHomClass.{max (max u1 u2) u3, max u1 u3, max (max u1 u2) u3} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4940 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.addZeroClass.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4940 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddEquivClass.instAddMonoidHomClass.{max (max u1 u2) u3, max u1 u3, max (max u1 u2) u3} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4940 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.addZeroClass.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4940 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddEquiv.instAddEquivClassAddEquiv.{max u1 u3, max (max u1 u2) u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4940 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (Finsupp.lift.{u1, u2, u3} M R _inst_1 _inst_3 _inst_4 X) f) g) (Finsupp.sum.{u3, u2, u1} X R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) _inst_3 g (fun (x : X) (r : R) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4))))) r (f x)))
Case conversion may be inaccurate. Consider using '#align finsupp.lift_apply Finsupp.lift_applyₓ'. -/
@[simp]
theorem lift_apply (f) (g) : ((lift M R X) f) g = g.Sum fun x r => r • f x :=
@@ -712,7 +712,7 @@ def lmapDomain (f : α → α') : (α →₀ M) →ₗ[R] α' →₀ M
lean 3 declaration is
forall {α : Type.{u1}} (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {α' : Type.{u4}} (f : α -> α') (l : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))), Eq.{max (succ u4) (succ u2)} (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (coeFn.{max (succ (max u1 u2)) (succ (max u4 u2)), max (succ (max u1 u2)) (succ (max u4 u2))} (LinearMap.{u3, u3, max u1 u2, max u4 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4)) (fun (_x : LinearMap.{u3, u3, max u1 u2, max u4 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4)) => (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) -> (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))))) (LinearMap.hasCoeToFun.{u3, u3, max u1 u2, max u4 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lmapDomain.{u1, u2, u3, u4} α M R _inst_1 _inst_3 _inst_4 α' f) l) (Finsupp.mapDomain.{u1, u4, u2} α α' M _inst_3 f l)
but is expected to have type
- forall {α : Type.{u4}} (M : Type.{u3}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u1, u3} R M _inst_1 _inst_3] {α' : Type.{u2}} (f : α -> α') (l : Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) l) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u3), max (succ u3) (succ u2)} (LinearMap.{u1, u1, max u3 u4, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.addCommMonoid.{u4, u3} α M _inst_3) (Finsupp.addCommMonoid.{u2, u3} α' M _inst_3) (Finsupp.module.{u4, u3, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u2, u3, u1} α' M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (fun (_x : Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max u3 u2} R R (Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} α M _inst_3) (Finsupp.addCommMonoid.{u2, u3} α' M _inst_3) (Finsupp.module.{u4, u3, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u2, u3, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lmapDomain.{u4, u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 α' f) l) (Finsupp.mapDomain.{u4, u2, u3} α α' M _inst_3 f l)
+ forall {α : Type.{u4}} (M : Type.{u3}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u1, u3} R M _inst_1 _inst_3] {α' : Type.{u2}} (f : α -> α') (l : Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) l) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u3), max (succ u3) (succ u2)} (LinearMap.{u1, u1, max u3 u4, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.addCommMonoid.{u4, u3} α M _inst_3) (Finsupp.addCommMonoid.{u2, u3} α' M _inst_3) (Finsupp.module.{u4, u3, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u2, u3, u1} α' M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (fun (_x : Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max u3 u2} R R (Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} α M _inst_3) (Finsupp.addCommMonoid.{u2, u3} α' M _inst_3) (Finsupp.module.{u4, u3, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u2, u3, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lmapDomain.{u4, u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 α' f) l) (Finsupp.mapDomain.{u4, u2, u3} α α' M _inst_3 f l)
Case conversion may be inaccurate. Consider using '#align finsupp.lmap_domain_apply Finsupp.lmapDomain_applyₓ'. -/
@[simp]
theorem lmapDomain_apply (f : α → α') (l : α →₀ M) :
@@ -865,7 +865,7 @@ variable {α M v}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {v : α -> M} (l : Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v) l) (Finsupp.sum.{u1, u3, u2} α R M (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 l (fun (i : α) (a : R) => SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) a (v i)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {v : α -> M} (l : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 v) l) (Finsupp.sum.{u3, u2, u1} α R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) _inst_3 l (fun (i : α) (a : R) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4))))) a (v i)))
+ forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {v : α -> M} (l : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 v) l) (Finsupp.sum.{u3, u2, u1} α R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) _inst_3 l (fun (i : α) (a : R) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4))))) a (v i)))
Case conversion may be inaccurate. Consider using '#align finsupp.total_apply Finsupp.total_applyₓ'. -/
theorem total_apply (l : α →₀ R) : Finsupp.total α M R v l = l.Sum fun i a => a • v i :=
rfl
@@ -875,7 +875,7 @@ theorem total_apply (l : α →₀ R) : Finsupp.total α M R v l = l.Sum fun i a
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {v : α -> M} {l : Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))} {s : Finset.{u1} α}, (Membership.Mem.{max u1 u3, max u1 u3} (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (SetLike.hasMem.{max u1 u3, max u1 u3} (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) (Submodule.setLike.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)))) l (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} α) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (Finset.Set.hasCoeT.{u1} α))) s))) -> (Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v) l) (Finset.sum.{u2, u1} M α _inst_3 s (fun (i : α) => SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (fun (_x : Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) => α -> R) (Finsupp.coeFun.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) l i) (v i))))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {v : α -> M} {l : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))} {s : Finset.{u3} α}, (Membership.mem.{max u3 u2, max u2 u3} (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (Submodule.instSetLikeSubmodule.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)))) l (Finsupp.supported.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1) (Finset.toSet.{u3} α s))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 v) l) (Finset.sum.{u1, u3} M α _inst_3 s (fun (i : α) => HSMul.hSMul.{u2, u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M M (instHSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (SMulZeroClass.toSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M _inst_1 _inst_3 _inst_4))))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) α (fun (_x : α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) _x) (Finsupp.funLike.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) l i) (v i))))
+ forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {v : α -> M} {l : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))} {s : Finset.{u3} α}, (Membership.mem.{max u3 u2, max u2 u3} (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (Submodule.instSetLikeSubmodule.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)))) l (Finsupp.supported.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1) (Finset.toSet.{u3} α s))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 v) l) (Finset.sum.{u1, u3} M α _inst_3 s (fun (i : α) => HSMul.hSMul.{u2, u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M M (instHSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (SMulZeroClass.toSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M _inst_1 _inst_3 _inst_4))))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) α (fun (_x : α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) _x) (Finsupp.funLike.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) l i) (v i))))
Case conversion may be inaccurate. Consider using '#align finsupp.total_apply_of_mem_supported Finsupp.total_apply_of_mem_supportedₓ'. -/
theorem total_apply_of_mem_supported {l : α →₀ R} {s : Finset α}
(hs : l ∈ supported R R (↑s : Set α)) : Finsupp.total α M R v l = s.Sum fun i => l i • v i :=
@@ -887,7 +887,7 @@ theorem total_apply_of_mem_supported {l : α →₀ R} {s : Finset α}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {v : α -> M} (c : R) (a : α), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v) (Finsupp.single.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) a c)) (SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) c (v a))
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u3}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u1, u3} R M _inst_1 _inst_3] {v : α -> M} (c : R) (a : α), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) (Finsupp.single.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) a c)) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u1), succ u3} (LinearMap.{u1, u1, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u3} R R (Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4 v) (Finsupp.single.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) a c)) (HSMul.hSMul.{u1, u3, u3} R M M (instHSMul.{u1, u3} R M (SMulZeroClass.toSMul.{u1, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u1, u3} R M _inst_1 _inst_3 _inst_4))))) c (v a))
+ forall {α : Type.{u2}} {M : Type.{u3}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u1, u3} R M _inst_1 _inst_3] {v : α -> M} (c : R) (a : α), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) (Finsupp.single.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) a c)) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u1), succ u3} (LinearMap.{u1, u1, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u3} R R (Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4 v) (Finsupp.single.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) a c)) (HSMul.hSMul.{u1, u3, u3} R M M (instHSMul.{u1, u3} R M (SMulZeroClass.toSMul.{u1, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u1, u3} R M _inst_1 _inst_3 _inst_4))))) c (v a))
Case conversion may be inaccurate. Consider using '#align finsupp.total_single Finsupp.total_singleₓ'. -/
@[simp]
theorem total_single (c : R) (a : α) : Finsupp.total α M R v (single a c) = c • v a := by
@@ -898,7 +898,7 @@ theorem total_single (c : R) (a : α) : Finsupp.total α M R v (single a c) = c
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (x : Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u1 u2} (α -> M) 0 (OfNat.mk.{max u1 u2} (α -> M) 0 (Zero.zero.{max u1 u2} (α -> M) (Pi.instZero.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))))))) x) (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))))))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u3 u1} (α -> M) 0 (Zero.toOfNat0.{max u3 u1} (α -> M) (Pi.instZero.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.6471 : α) => M) (fun (i : α) => AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) _inst_3))))
+ forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u3 u1} (α -> M) 0 (Zero.toOfNat0.{max u3 u1} (α -> M) (Pi.instZero.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.6502 : α) => M) (fun (i : α) => AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) _inst_3))))
Case conversion may be inaccurate. Consider using '#align finsupp.total_zero_apply Finsupp.total_zero_applyₓ'. -/
theorem total_zero_apply (x : α →₀ R) : (Finsupp.total α M R 0) x = 0 := by
simp [Finsupp.total_apply]
@@ -910,7 +910,7 @@ variable (α M)
lean 3 declaration is
forall (α : Type.{u1}) (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], Eq.{max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u1 u2} (α -> M) 0 (OfNat.mk.{max u1 u2} (α -> M) 0 (Zero.zero.{max u1 u2} (α -> M) (Pi.instZero.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))))))) (OfNat.ofNat.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) 0 (OfNat.mk.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) 0 (Zero.zero.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.hasZero.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))
but is expected to have type
- forall (α : Type.{u3}) (M : Type.{u2}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Eq.{max (max (succ u3) (succ u2)) (succ u1)} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u3 u2} (α -> M) 0 (Zero.toOfNat0.{max u3 u2} (α -> M) (Pi.instZero.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.6471 : α) => M) (fun (i : α) => AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))))) (OfNat.ofNat.{max (max u3 u2) u1} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) 0 (Zero.toOfNat0.{max (max u3 u2) u1} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (LinearMap.instZeroLinearMap.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))
+ forall (α : Type.{u3}) (M : Type.{u2}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Eq.{max (max (succ u3) (succ u2)) (succ u1)} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u3 u2} (α -> M) 0 (Zero.toOfNat0.{max u3 u2} (α -> M) (Pi.instZero.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.6502 : α) => M) (fun (i : α) => AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))))) (OfNat.ofNat.{max (max u3 u2) u1} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) 0 (Zero.toOfNat0.{max (max u3 u2) u1} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (LinearMap.instZeroLinearMap.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))
Case conversion may be inaccurate. Consider using '#align finsupp.total_zero Finsupp.total_zeroₓ'. -/
@[simp]
theorem total_zero : Finsupp.total α M R 0 = 0 :=
@@ -923,7 +923,7 @@ variable {α M}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {M' : Type.{u4}} [_inst_9 : AddCommMonoid.{u4} M'] [_inst_10 : Module.{u3, u4} R M' _inst_1 _inst_9] (f : LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_3 _inst_9 _inst_4 _inst_10) (v : α -> M) (l : Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))), Eq.{succ u4} M' (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_3 _inst_9 _inst_4 _inst_10) (fun (_x : LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_3 _inst_9 _inst_4 _inst_10) => M -> M') (LinearMap.hasCoeToFun.{u3, u3, u2, u4} R R M M' _inst_1 _inst_1 _inst_3 _inst_9 _inst_4 _inst_10 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v) l)) (coeFn.{max (succ (max u1 u3)) (succ u4), max (succ (max u1 u3)) (succ u4)} (LinearMap.{u3, u3, max u1 u3, 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(x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, u2} R R M _inst_1 _inst_3 _inst_3 M' _inst_4 _inst_10 _inst_9 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_3))) f) v)) l)
Case conversion may be inaccurate. Consider using '#align finsupp.apply_total Finsupp.apply_totalₓ'. -/
theorem apply_total (f : M →ₗ[R] M') (v) (l : α →₀ R) :
f (Finsupp.total α M R v l) = Finsupp.total α M' R (f ∘ v) l := by
@@ -934,7 +934,7 @@ theorem apply_total (f : M →ₗ[R] M') (v) (l : α →₀ R) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] [_inst_11 : Unique.{succ u1} α] (l : Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (v : α -> M), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v) l) (SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (fun (_x : Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) => α -> R) (Finsupp.coeFun.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) l (Inhabited.default.{succ u1} α (Unique.inhabited.{succ u1} α _inst_11))) (v (Inhabited.default.{succ u1} α (Unique.inhabited.{succ u1} α _inst_11))))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] [_inst_11 : Unique.{succ u3} α] (l : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (v : α -> M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 v) l) (HSMul.hSMul.{u2, u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M M (instHSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M (SMulZeroClass.toSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M _inst_1 _inst_3 _inst_4))))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) α (fun (_x : α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) _x) (Finsupp.funLike.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) l (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) (v (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))))
+ forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] [_inst_11 : Unique.{succ u3} α] (l : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (v : α -> M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 v) l) (HSMul.hSMul.{u2, u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M M (instHSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M (SMulZeroClass.toSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M _inst_1 _inst_3 _inst_4))))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) α (fun (_x : α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) _x) (Finsupp.funLike.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) l (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) (v (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))))
Case conversion may be inaccurate. Consider using '#align finsupp.total_unique Finsupp.total_uniqueₓ'. -/
theorem total_unique [Unique α] (l : α →₀ R) (v) :
Finsupp.total α M R v l = l default • v default := by rw [← total_single, ← unique_single l]
@@ -944,7 +944,7 @@ theorem total_unique [Unique α] (l : α →₀ R) (v) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {v : α -> M}, (Function.Surjective.{succ u1, succ u2} α M v) -> (Function.Surjective.{max (succ u1) (succ u3), succ u2} (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {v : α -> M}, (Function.Surjective.{succ u3, succ u2} α M v) -> (Function.Surjective.{max (succ u3) (succ u1), succ u2} (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u1), succ u2} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 v)))
+ forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {v : α -> M}, (Function.Surjective.{succ u3, succ u2} α M v) -> (Function.Surjective.{max (succ u3) (succ u1), succ u2} (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u1), succ u2} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 v)))
Case conversion may be inaccurate. Consider using '#align finsupp.total_surjective Finsupp.total_surjectiveₓ'. -/
theorem total_surjective (h : Function.Surjective v) :
Function.Surjective (Finsupp.total α M R v) :=
@@ -968,7 +968,7 @@ theorem total_range (h : Function.Surjective v) : (Finsupp.total α M R v).range
lean 3 declaration is
forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] (M : Type.{u2}) [_inst_11 : AddCommMonoid.{u2} M] [_inst_12 : Module.{u1, u2} R M _inst_1 _inst_11], Function.Surjective.{max (succ u2) (succ u1), succ u2} (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (coeFn.{max (succ (max u2 u1)) (succ u2), max (succ (max u2 u1)) (succ u2)} (LinearMap.{u1, u1, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_11 (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_12) (fun (_x : LinearMap.{u1, u1, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_11 (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_12) => (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u2} R R (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_11 (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_12 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} M M R _inst_1 _inst_11 _inst_12 (id.{succ u2} M)))
but is expected to have type
- forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] (M : Type.{u2}) [_inst_11 : AddCommMonoid.{u2} M] [_inst_12 : Module.{u1, u2} R M _inst_1 _inst_11], Function.Surjective.{max (succ u1) (succ u2), succ u2} (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_11 (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_12) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u2} R R (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_11 (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_12 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} M M R _inst_1 _inst_11 _inst_12 (id.{succ u2} M)))
+ forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] (M : Type.{u2}) [_inst_11 : AddCommMonoid.{u2} M] [_inst_12 : Module.{u1, u2} R M _inst_1 _inst_11], Function.Surjective.{max (succ u1) (succ u2), succ u2} (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_11 (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_12) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u2} R R (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_11 (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_12 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} M M R _inst_1 _inst_11 _inst_12 (id.{succ u2} M)))
Case conversion may be inaccurate. Consider using '#align finsupp.total_id_surjective Finsupp.total_id_surjectiveₓ'. -/
/-- Any module is a quotient of a free module. This is stated as surjectivity of
`finsupp.total M M R id : (M →₀ R) →ₗ[R] M`. -/
@@ -1005,7 +1005,7 @@ theorem range_total : (Finsupp.total α M R v).range = span R (range v) :=
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {α' : Type.{u4}} {M' : Type.{u5}} [_inst_9 : AddCommMonoid.{u5} M'] [_inst_10 : Module.{u3, u5} R M' _inst_1 _inst_9] {v : α -> M} {v' : α' -> M'} (f : α -> α') (g : LinearMap.{u3, u3, u2, u5} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_3 _inst_9 _inst_4 _inst_10), (forall (i : α), Eq.{succ u5} M' (coeFn.{max (succ u2) (succ u5), max (succ u2) (succ u5)} (LinearMap.{u3, u3, u2, u5} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_3 _inst_9 _inst_4 _inst_10) (fun (_x : LinearMap.{u3, u3, u2, u5} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_3 _inst_9 _inst_4 _inst_10) => M -> M') (LinearMap.hasCoeToFun.{u3, u3, u2, u5} R R M M' _inst_1 _inst_1 _inst_3 _inst_9 _inst_4 _inst_10 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) g (v i)) (v' (f i))) -> (Eq.{max (succ (max u1 u3)) (succ u5)} (LinearMap.{u3, u3, max u1 u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) M' (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_10) (LinearMap.comp.{u3, u3, u3, max u1 u3, max u4 u3, u5} R R R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) (Finsupp.{u4, u3} α' R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M' _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.addCommMonoid.{u4, u3} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Finsupp.module.{u4, u3, u3} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_10 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomCompTriple.right_ids.{u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u4, u5, u3} α' M' R _inst_1 _inst_9 _inst_10 v') (Finsupp.lmapDomain.{u1, u3, u3, u4} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) α' f)) (LinearMap.comp.{u3, u3, u3, max u1 u3, u2, u5} R R R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) M M' _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 _inst_9 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 _inst_10 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomCompTriple.right_ids.{u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) g (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v)))
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u4}} (R : Type.{u5}) {_inst_1 : Type.{u1}} {_inst_3 : Type.{u3}} [_inst_4 : Semiring.{u5} R] [α' : AddCommMonoid.{u3} _inst_3] [M' : AddCommMonoid.{u4} M] [_inst_9 : Module.{u5, u3} R _inst_3 _inst_4 α'] [_inst_10 : Module.{u5, u4} R M _inst_4 M'] {v : α -> M} {v' : _inst_1 -> _inst_3} (f : α -> _inst_1) (g : LinearMap.{u5, u5, u4, u3} R R _inst_4 _inst_4 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) M _inst_3 M' α' _inst_10 _inst_9), (forall (i : α), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => _inst_3) (v i)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_4 _inst_4 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) M _inst_3 M' α' _inst_10 _inst_9) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M _inst_3 _inst_4 _inst_4 M' α' _inst_10 _inst_9 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) g (v i)) (v' (f i))) -> (Eq.{max (max (succ u2) (succ u5)) (succ u3)} (LinearMap.{u5, u5, max u5 u2, u3} R R _inst_4 _inst_4 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (Finsupp.{u2, u5} α R (AddMonoid.toZero.{u5} R (AddCommMonoid.toAddMonoid.{u5} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))))) _inst_3 (Finsupp.addCommMonoid.{u2, u5} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))) α' (Finsupp.module.{u2, u5, u5} α R R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Semiring.toModule.{u5} R _inst_4)) _inst_9) (LinearMap.comp.{u5, u5, u5, max u5 u2, max u5 u1, u3} R R R (Finsupp.{u2, u5} α R (AddMonoid.toZero.{u5} R (AddCommMonoid.toAddMonoid.{u5} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))))) (Finsupp.{u1, u5} _inst_1 R (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_4))) _inst_3 _inst_4 _inst_4 _inst_4 (Finsupp.addCommMonoid.{u2, u5} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))) (Finsupp.addCommMonoid.{u1, u5} _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))) α' (Finsupp.module.{u2, u5, u5} α R R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Semiring.toModule.{u5} R _inst_4)) (Finsupp.module.{u1, u5, u5} _inst_1 R R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Semiring.toModule.{u5} R _inst_4)) _inst_9 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHomCompTriple.ids.{u5, u5} R R _inst_4 _inst_4 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Finsupp.total.{u1, u3, u5} _inst_1 _inst_3 R _inst_4 α' _inst_9 v') (Finsupp.lmapDomain.{u2, u5, u5, u1} α R R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Semiring.toModule.{u5} R _inst_4) _inst_1 f)) (LinearMap.comp.{u5, u5, u5, max u2 u5, u4, u3} R R R (Finsupp.{u2, u5} α R (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_4))) M _inst_3 _inst_4 _inst_4 _inst_4 (Finsupp.addCommMonoid.{u2, u5} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))) M' α' (Finsupp.module.{u2, u5, u5} α R R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Semiring.toModule.{u5} R _inst_4)) _inst_10 _inst_9 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHomCompTriple.ids.{u5, u5} R R _inst_4 _inst_4 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) g (Finsupp.total.{u2, u4, u5} α M R _inst_4 M' _inst_10 v)))
+ forall {α : Type.{u2}} {M : Type.{u4}} (R : Type.{u5}) {_inst_1 : Type.{u1}} {_inst_3 : Type.{u3}} [_inst_4 : Semiring.{u5} R] [α' : AddCommMonoid.{u3} _inst_3] [M' : AddCommMonoid.{u4} M] [_inst_9 : Module.{u5, u3} R _inst_3 _inst_4 α'] [_inst_10 : Module.{u5, u4} R M _inst_4 M'] {v : α -> M} {v' : _inst_1 -> _inst_3} (f : α -> _inst_1) (g : LinearMap.{u5, u5, u4, u3} R R _inst_4 _inst_4 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) M _inst_3 M' α' _inst_10 _inst_9), (forall (i : α), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => _inst_3) (v i)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_4 _inst_4 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) M _inst_3 M' α' _inst_10 _inst_9) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M _inst_3 _inst_4 _inst_4 M' α' _inst_10 _inst_9 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) g (v i)) (v' (f i))) -> (Eq.{max (max (succ u2) (succ u5)) (succ u3)} (LinearMap.{u5, u5, max u5 u2, u3} R R _inst_4 _inst_4 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (Finsupp.{u2, u5} α R (AddMonoid.toZero.{u5} R (AddCommMonoid.toAddMonoid.{u5} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))))) _inst_3 (Finsupp.addCommMonoid.{u2, u5} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))) α' (Finsupp.module.{u2, u5, u5} α R R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Semiring.toModule.{u5} R _inst_4)) _inst_9) (LinearMap.comp.{u5, u5, u5, max u5 u2, max u5 u1, u3} R R R (Finsupp.{u2, u5} α R (AddMonoid.toZero.{u5} R (AddCommMonoid.toAddMonoid.{u5} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))))) (Finsupp.{u1, u5} _inst_1 R (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_4))) _inst_3 _inst_4 _inst_4 _inst_4 (Finsupp.addCommMonoid.{u2, u5} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))) (Finsupp.addCommMonoid.{u1, u5} _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))) α' (Finsupp.module.{u2, u5, u5} α R R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Semiring.toModule.{u5} R _inst_4)) (Finsupp.module.{u1, u5, u5} _inst_1 R R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Semiring.toModule.{u5} R _inst_4)) _inst_9 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHomCompTriple.ids.{u5, u5} R R _inst_4 _inst_4 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Finsupp.total.{u1, u3, u5} _inst_1 _inst_3 R _inst_4 α' _inst_9 v') (Finsupp.lmapDomain.{u2, u5, u5, u1} α R R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Semiring.toModule.{u5} R _inst_4) _inst_1 f)) (LinearMap.comp.{u5, u5, u5, max u2 u5, u4, u3} R R R (Finsupp.{u2, u5} α R (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_4))) M _inst_3 _inst_4 _inst_4 _inst_4 (Finsupp.addCommMonoid.{u2, u5} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))) M' α' (Finsupp.module.{u2, u5, u5} α R R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Semiring.toModule.{u5} R _inst_4)) _inst_10 _inst_9 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHomCompTriple.ids.{u5, u5} R R _inst_4 _inst_4 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) g (Finsupp.total.{u2, u4, u5} α M R _inst_4 M' _inst_10 v)))
Case conversion may be inaccurate. Consider using '#align finsupp.lmap_domain_total Finsupp.lmapDomain_totalₓ'. -/
theorem lmapDomain_total (f : α → α') (g : M →ₗ[R] M') (h : ∀ i, g (v i) = v' (f i)) :
(Finsupp.total α' M' R v').comp (lmapDomain R R f) = g.comp (Finsupp.total α M R v) := by
@@ -1029,7 +1029,7 @@ theorem total_comp_lmapDomain (f : α → α') :
lean 3 declaration is
forall {α : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] {α' : Type.{u3}} {M' : Type.{u4}} [_inst_9 : AddCommMonoid.{u4} M'] [_inst_10 : Module.{u2, u4} R M' _inst_1 _inst_9] {v' : α' -> M'} (f : Function.Embedding.{succ u1, succ u3} α α') (l : Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))), Eq.{succ u4} M' (coeFn.{max (succ (max u3 u2)) (succ u4), max (succ (max u3 u2)) (succ u4)} (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) (fun (_x : LinearMap.{u2, u2, max u3 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) => (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M') (LinearMap.hasCoeToFun.{u2, u2, max u3 u2, u4} R R (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u4, u2} α' M' R _inst_1 _inst_9 _inst_10 v') (Finsupp.embDomain.{u1, u3, u2} α α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) f l)) (coeFn.{max (succ (max u1 u2)) (succ u4), max (succ (max u1 u2)) (succ u4)} (LinearMap.{u2, u2, max u1 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) (fun (_x : LinearMap.{u2, u2, max u1 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) => (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M') (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u4} R R (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u1, u4, u2} α M' R _inst_1 _inst_9 _inst_10 (Function.comp.{succ u1, succ u3, succ u4} α α' M' v' (coeFn.{max 1 (succ u1) (succ u3), max (succ u1) (succ u3)} (Function.Embedding.{succ u1, succ u3} α α') (fun (_x : Function.Embedding.{succ u1, succ u3} α α') => α -> α') (Function.Embedding.hasCoeToFun.{succ u1, succ u3} α α') f))) l)
but is expected to have type
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+ forall {α : Type.{u4}} (R : Type.{u2}) {_inst_1 : Type.{u3}} {α' : Type.{u1}} [M' : Semiring.{u2} R] [_inst_9 : AddCommMonoid.{u1} α'] [_inst_10 : Module.{u2, u1} R α' M' _inst_9] {v' : _inst_1 -> α'} (f : Function.Embedding.{succ u4, succ u3} α _inst_1) (l : Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) => α') (Finsupp.embDomain.{u4, u3, u2} α _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M')) f l)) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R M' M' (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')) (Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) α' (Finsupp.addCommMonoid.{u3, u2} _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')))) _inst_9 (Finsupp.module.{u3, u2, u2} _inst_1 R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Semiring.toModule.{u2} R M')) _inst_10) (Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) (fun (_x : Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) => α') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) α' M' M' (Finsupp.addCommMonoid.{u3, u2} _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')))) _inst_9 (Finsupp.module.{u3, u2, u2} _inst_1 R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Semiring.toModule.{u2} R M')) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Finsupp.total.{u3, u1, u2} _inst_1 α' R M' _inst_9 _inst_10 v') (Finsupp.embDomain.{u4, u3, u2} α _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M')) f l)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u1), max (succ u4) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u4, u1} R R M' M' (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) α' (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')))) _inst_9 (Finsupp.module.{u4, u2, u2} α R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Semiring.toModule.{u2} R M')) _inst_10) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) (fun (_x : Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) => α') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u1} R R (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) α' M' M' (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')))) _inst_9 (Finsupp.module.{u4, u2, u2} α R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Semiring.toModule.{u2} R M')) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Finsupp.total.{u4, u1, u2} α α' R M' _inst_9 _inst_10 (Function.comp.{succ u4, succ u3, succ u1} α _inst_1 α' v' (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Function.Embedding.{succ u4, succ u3} α _inst_1) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => _inst_1) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u3), succ u4, succ u3} (Function.Embedding.{succ u4, succ u3} α _inst_1) α _inst_1 (Function.instEmbeddingLikeEmbedding.{succ u4, succ u3} α _inst_1)) f))) l)
Case conversion may be inaccurate. Consider using '#align finsupp.total_emb_domain Finsupp.total_embDomainₓ'. -/
@[simp]
theorem total_embDomain (f : α ↪ α') (l : α →₀ R) :
@@ -1041,7 +1041,7 @@ theorem total_embDomain (f : α ↪ α') (l : α →₀ R) :
lean 3 declaration is
forall {α : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] {α' : Type.{u3}} {M' : Type.{u4}} [_inst_9 : AddCommMonoid.{u4} M'] [_inst_10 : Module.{u2, u4} R M' _inst_1 _inst_9] {v' : α' -> M'} (f : α -> α') (l : Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))), Eq.{succ u4} M' (coeFn.{max (succ (max u3 u2)) (succ u4), max (succ (max u3 u2)) (succ u4)} (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) (fun (_x : LinearMap.{u2, u2, max u3 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) => (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M') (LinearMap.hasCoeToFun.{u2, u2, max u3 u2, u4} R R (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u4, u2} α' M' R _inst_1 _inst_9 _inst_10 v') (Finsupp.mapDomain.{u1, u3, u2} α α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f l)) (coeFn.{max (succ (max u1 u2)) (succ u4), max (succ (max u1 u2)) (succ u4)} (LinearMap.{u2, u2, max u1 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) (fun (_x : LinearMap.{u2, u2, max u1 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) => (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M') (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u4} R R (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u1, u4, u2} α M' R _inst_1 _inst_9 _inst_10 (Function.comp.{succ u1, succ u3, succ u4} α α' M' v' f)) l)
but is expected to have type
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+ forall {α : Type.{u4}} (R : Type.{u3}) {_inst_1 : Type.{u1}} {α' : Type.{u2}} [M' : Semiring.{u3} R] [_inst_9 : AddCommMonoid.{u2} α'] [_inst_10 : Module.{u3, u2} R α' M' _inst_9] {v' : _inst_1 -> α'} (f : α -> _inst_1) (l : Finsupp.{u4, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) => α') (Finsupp.mapDomain.{u4, u1, u3} α _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) f l)) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u1), succ u2} (LinearMap.{u3, u3, max u3 u1, u2} R R M' M' (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')) (Finsupp.{u1, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) α' (Finsupp.addCommMonoid.{u1, u3} _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')))) _inst_9 (Finsupp.module.{u1, u3, u3} _inst_1 R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) (Semiring.toModule.{u3} R M')) _inst_10) (Finsupp.{u1, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) (fun (_x : Finsupp.{u1, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) => α') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u1, u2} R R (Finsupp.{u1, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) α' M' M' (Finsupp.addCommMonoid.{u1, u3} _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')))) _inst_9 (Finsupp.module.{u1, u3, u3} _inst_1 R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) (Semiring.toModule.{u3} R M')) _inst_10 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) (Finsupp.total.{u1, u2, u3} _inst_1 α' R M' _inst_9 _inst_10 v') (Finsupp.mapDomain.{u4, u1, u3} α _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) f l)) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} R R M' M' (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')) (Finsupp.{u4, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) α' (Finsupp.addCommMonoid.{u4, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')))) _inst_9 (Finsupp.module.{u4, u3, u3} α R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) (Semiring.toModule.{u3} R M')) _inst_10) (Finsupp.{u4, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) (fun (_x : Finsupp.{u4, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u4, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) => α') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} R R (Finsupp.{u4, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) α' M' M' (Finsupp.addCommMonoid.{u4, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')))) _inst_9 (Finsupp.module.{u4, u3, u3} α R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) (Semiring.toModule.{u3} R M')) _inst_10 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) (Finsupp.total.{u4, u2, u3} α α' R M' _inst_9 _inst_10 (Function.comp.{succ u4, succ u1, succ u2} α _inst_1 α' v' f)) l)
Case conversion may be inaccurate. Consider using '#align finsupp.total_map_domain Finsupp.total_mapDomainₓ'. -/
@[simp]
theorem total_mapDomain (f : α → α') (l : α →₀ R) :
@@ -1053,7 +1053,7 @@ theorem total_mapDomain (f : α → α') (l : α →₀ R) :
lean 3 declaration is
forall {α : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] {α' : Type.{u3}} {M' : Type.{u4}} [_inst_9 : AddCommMonoid.{u4} M'] [_inst_10 : Module.{u2, u4} R M' _inst_1 _inst_9] {v' : α' -> M'} (f : Equiv.{succ u1, succ u3} α α') (l : Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))), Eq.{succ u4} M' (coeFn.{max (succ (max u3 u2)) (succ u4), max (succ (max u3 u2)) (succ u4)} (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) (fun (_x : LinearMap.{u2, u2, max u3 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) => (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M') (LinearMap.hasCoeToFun.{u2, u2, max u3 u2, u4} R R (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u4, u2} α' M' R _inst_1 _inst_9 _inst_10 v') (Finsupp.equivMapDomain.{u1, u3, u2} α α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) f l)) (coeFn.{max (succ (max u1 u2)) (succ u4), max (succ (max u1 u2)) (succ u4)} (LinearMap.{u2, u2, max u1 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) (fun (_x : LinearMap.{u2, u2, max u1 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) => (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M') (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u4} R R (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u1, u4, u2} α M' R _inst_1 _inst_9 _inst_10 (Function.comp.{succ u1, succ u3, succ u4} α α' M' v' (coeFn.{max 1 (max (succ u1) (succ u3)) (succ u3) (succ u1), max (succ u1) (succ u3)} (Equiv.{succ u1, succ u3} α α') (fun (_x : Equiv.{succ u1, succ u3} α α') => α -> α') (Equiv.hasCoeToFun.{succ u1, succ u3} α α') f))) l)
but is expected to have type
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+ forall {α : Type.{u4}} (R : Type.{u2}) {_inst_1 : Type.{u3}} {α' : Type.{u1}} [M' : Semiring.{u2} R] [_inst_9 : AddCommMonoid.{u1} α'] [_inst_10 : Module.{u2, u1} R α' M' _inst_9] {v' : _inst_1 -> α'} (f : Equiv.{succ u4, succ u3} α _inst_1) (l : Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) => α') (Finsupp.equivMapDomain.{u4, u3, u2} α _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M')) f l)) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R M' M' (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')) (Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) α' (Finsupp.addCommMonoid.{u3, u2} _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')))) _inst_9 (Finsupp.module.{u3, u2, u2} _inst_1 R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Semiring.toModule.{u2} R M')) _inst_10) (Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) (fun (_x : Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) => α') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) α' M' M' (Finsupp.addCommMonoid.{u3, u2} _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')))) _inst_9 (Finsupp.module.{u3, u2, u2} _inst_1 R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Semiring.toModule.{u2} R M')) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Finsupp.total.{u3, u1, u2} _inst_1 α' R M' _inst_9 _inst_10 v') (Finsupp.equivMapDomain.{u4, u3, u2} α _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M')) f l)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u1), max (succ u4) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u4, u1} R R M' M' (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) α' (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')))) _inst_9 (Finsupp.module.{u4, u2, u2} α R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Semiring.toModule.{u2} R M')) _inst_10) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) (fun (_x : Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) => α') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u1} R R (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) α' M' M' (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')))) _inst_9 (Finsupp.module.{u4, u2, u2} α R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Semiring.toModule.{u2} R M')) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Finsupp.total.{u4, u1, u2} α α' R M' _inst_9 _inst_10 (Function.comp.{succ u4, succ u3, succ u1} α _inst_1 α' v' (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Equiv.{succ u4, succ u3} α _inst_1) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => _inst_1) _x) (Equiv.instFunLikeEquiv.{succ u4, succ u3} α _inst_1) f))) l)
Case conversion may be inaccurate. Consider using '#align finsupp.total_equiv_map_domain Finsupp.total_equivMapDomainₓ'. -/
@[simp]
theorem total_equivMapDomain (f : α ≃ α') (l : α →₀ R) :
@@ -1076,7 +1076,7 @@ theorem span_eq_range_total (s : Set M) : span R s = (Finsupp.total s M R coe).r
lean 3 declaration is
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but is expected to have type
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+ forall {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u2} M) (x : M), Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 s)) (Exists.{max (succ u2) (succ u1)} (Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (l : Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} (Set.Elem.{u2} M s) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u1, u1} (Set.Elem.{u2} M s) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u2} R R (Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} (Set.Elem.{u2} M s) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u1, u1} (Set.Elem.{u2} M s) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} (Set.Elem.{u2} M s) M R _inst_1 _inst_3 _inst_4 (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s))) l) x))
Case conversion may be inaccurate. Consider using '#align finsupp.mem_span_iff_total Finsupp.mem_span_iff_totalₓ'. -/
theorem mem_span_iff_total (s : Set M) (x : M) :
x ∈ span R s ↔ ∃ l : s →₀ R, Finsupp.total s M R coe l = x :=
@@ -1128,7 +1128,7 @@ theorem span_image_eq_map_total (s : Set α) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {v : α -> M} {s : Set.{u1} α} {x : M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u3, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s))) (Exists.{succ (max u1 u3)} (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (fun (l : Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) => Exists.{0} (Membership.Mem.{max u1 u3, max u1 u3} (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (SetLike.hasMem.{max u1 u3, max u1 u3} (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) (Submodule.setLike.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)))) l (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s)) (fun (H : Membership.Mem.{max u1 u3, max u1 u3} (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (SetLike.hasMem.{max u1 u3, max u1 u3} (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) (Submodule.setLike.{u3, max 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v) l) x)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {v : α -> M} {s : Set.{u3} α} {x : M}, Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (Exists.{succ (max u3 u1)} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (fun (l : Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) => And (Membership.mem.{max u3 u1, max u1 u3} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{max u3 u1, max u3 u1} (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.instSetLikeSubmodule.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) l (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u1), succ u2} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (a : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) a) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 v) l) x)))
+ forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {v : α -> M} {s : Set.{u3} α} {x : M}, Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (Exists.{succ (max u3 u1)} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (fun (l : Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) => And (Membership.mem.{max u3 u1, max u1 u3} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{max u3 u1, max u3 u1} (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.instSetLikeSubmodule.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) l (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u1), succ u2} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (a : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) a) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 v) l) x)))
Case conversion may be inaccurate. Consider using '#align finsupp.mem_span_image_iff_total Finsupp.mem_span_image_iff_totalₓ'. -/
theorem mem_span_image_iff_total {s : Set α} {x : M} :
x ∈ span R (v '' s) ↔ ∃ l ∈ supported R R s, Finsupp.total α M R v l = x :=
@@ -1141,7 +1141,7 @@ theorem mem_span_image_iff_total {s : Set α} {x : M} :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (v : (Option.{u1} α) -> M) (f : Finsupp.{u1, u3} (Option.{u1} α) R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} (Option.{u1} α) R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} (Option.{u1} α) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} (Option.{u1} α) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} (Option.{u1} α) R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} (Option.{u1} α) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} (Option.{u1} α) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} (Option.{u1} α) R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} (Option.{u1} α) R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} (Option.{u1} α) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} (Option.{u1} α) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} (Option.{u1} α) M R _inst_1 _inst_3 _inst_4 v) f) (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M 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but is expected to have type
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+ forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (v : (Option.{u3} α) -> M) (f : Finsupp.{u3, u2} (Option.{u3} α) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} (Option.{u3} α) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) f) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} (Option.{u3} α) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} (Option.{u3} α) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R 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Case conversion may be inaccurate. Consider using '#align finsupp.total_option Finsupp.total_optionₓ'. -/
theorem total_option (v : Option α → M) (f : Option α →₀ R) :
Finsupp.total (Option α) M R v f =
@@ -1153,7 +1153,7 @@ theorem total_option (v : Option α → M) (f : Option α →₀ R) :
lean 3 declaration is
forall {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {α : Type.{u3}} {β : Type.{u4}} (A : α -> M) (B : β -> (Finsupp.{u3, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (f : Finsupp.{u4, u2} β R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))), Eq.{succ u1} M (coeFn.{max (succ (max u3 u2)) (succ u1), max (succ (max u3 u2)) (succ u1)} (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R 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+ forall {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {α : Type.{u4}} {β : Type.{u3}} (A : α -> M) (B : β -> (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))) (f : Finsupp.{u3, u2} β R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u3), max (succ u2) (succ u4)} (LinearMap.{u2, u2, max u2 u3, max u2 u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} β R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} β R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Finsupp.module.{u4, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, max u2 u4, u2} β (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) R 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Case conversion may be inaccurate. Consider using '#align finsupp.total_total Finsupp.total_totalₓ'. -/
theorem total_total {α β : Type _} (A : α → M) (B : β → α →₀ R) (f : β →₀ R) :
Finsupp.total α M R A (Finsupp.total β (α →₀ R) R B f) =
@@ -1230,7 +1230,7 @@ theorem total_comp (f : α' → α) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {α' : Type.{u4}} {v : α -> M} (f : α -> α') (l : Finsupp.{u4, u3} α' R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (hf : Set.InjOn.{u1, u4} α α' f (Set.preimage.{u1, u4} α α' f ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} α') (Set.{u4} α') (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} α') (Set.{u4} α') (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} α') (Set.{u4} α') (Finset.Set.hasCoeT.{u4} α'))) (Finsupp.support.{u4, u3} α' R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) l)))), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v) (Finsupp.comapDomain.{u1, u4, u3} α α' R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) f l hf)) (Finset.sum.{u2, u1} M α _inst_3 (Finset.preimage.{u1, u4} α α' (Finsupp.support.{u4, u3} α' R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) l) f hf) (fun (i : α) => SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) (coeFn.{max (succ u4) (succ u3), max (succ 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but is expected to have type
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+ forall {α : Type.{u2}} {M : Type.{u1}} (R : Type.{u3}) {_inst_1 : Type.{u4}} [_inst_3 : Semiring.{u3} R] [_inst_4 : AddCommMonoid.{u1} M] [α' : Module.{u3, u1} R M _inst_3 _inst_4] {v : α -> M} (f : α -> _inst_1) (l : Finsupp.{u4, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) (hf : Set.InjOn.{u2, u4} α _inst_1 f (Set.preimage.{u2, u4} α _inst_1 f (Finset.toSet.{u4} _inst_1 (Finsupp.support.{u4, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3)) l)))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) => M) (Finsupp.comapDomain.{u2, u4, u3} α _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3)) f l hf)) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_3 _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3)) (Finsupp.{u2, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) M (Finsupp.addCommMonoid.{u2, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3)))) _inst_4 (Finsupp.module.{u2, u3, u3} α R R _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3))) (Semiring.toModule.{u3} R _inst_3)) α') (Finsupp.{u2, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) (fun (_x : Finsupp.{u2, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) => M) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u1} R R (Finsupp.{u2, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) M _inst_3 _inst_3 (Finsupp.addCommMonoid.{u2, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3)))) _inst_4 (Finsupp.module.{u2, u3, u3} α R R _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3))) (Semiring.toModule.{u3} R _inst_3)) α' (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3))) (Finsupp.total.{u2, u1, u3} α M R _inst_3 _inst_4 α' v) (Finsupp.comapDomain.{u2, u4, u3} α _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3)) f l hf)) (Finset.sum.{u1, u2} M α _inst_4 (Finset.preimage.{u2, u4} α _inst_1 (Finsupp.support.{u4, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3)) l) f hf) (fun (i : α) => HSMul.hSMul.{u3, u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) M M (instHSMul.{u3, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) M (SMulZeroClass.toSMul.{u3, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u3, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) M (MonoidWithZero.toZero.{u3} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) _inst_3)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u3, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) M (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) _inst_3) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (Module.toMulActionWithZero.{u3, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) M _inst_3 _inst_4 α'))))) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Finsupp.{u4, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) _inst_1 (fun (_x : _inst_1) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) _x) (Finsupp.funLike.{u4, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) l (f i)) (v i)))
Case conversion may be inaccurate. Consider using '#align finsupp.total_comap_domain Finsupp.total_comapDomainₓ'. -/
theorem total_comapDomain (f : α → α') (l : α' →₀ R) (hf : Set.InjOn f (f ⁻¹' ↑l.support)) :
Finsupp.total α M R v (Finsupp.comapDomain f l hf) =
@@ -1242,7 +1242,7 @@ theorem total_comapDomain (f : α → α') (l : α' →₀ R) (hf : Set.InjOn f
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {s : Finset.{u1} α} {f : α -> R} (g : α -> M) (hf : forall (a : α), (Ne.{succ u3} R (f a) (OfNat.ofNat.{u3} R 0 (OfNat.mk.{u3} R 0 (Zero.zero.{u3} R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))))) -> (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s)), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 g) (Finsupp.onFinset.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) s f hf)) (Finset.sum.{u2, u1} M α _inst_3 s (fun (x : α) => SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) (f x) (g x)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {s : Finset.{u3} α} {f : α -> R} (g : α -> M) (hf : forall (a : α), (Ne.{succ u2} R (f a) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))))) -> (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) (Finsupp.onFinset.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) s f hf)) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 g) (Finsupp.onFinset.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) s f hf)) (Finset.sum.{u1, u3} M α _inst_3 s (fun (x : α) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4))))) (f x) (g x)))
+ forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {s : Finset.{u3} α} {f : α -> R} (g : α -> M) (hf : forall (a : α), (Ne.{succ u2} R (f a) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))))) -> (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) (Finsupp.onFinset.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) s f hf)) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 g) (Finsupp.onFinset.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) s f hf)) (Finset.sum.{u1, u3} M α _inst_3 s (fun (x : α) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4))))) (f x) (g x)))
Case conversion may be inaccurate. Consider using '#align finsupp.total_on_finset Finsupp.total_onFinsetₓ'. -/
theorem total_onFinset {s : Finset α} {f : α → R} (g : α → M) (hf : ∀ a, f a ≠ 0 → a ∈ s) :
Finsupp.total α M R g (Finsupp.onFinset s f hf) = Finset.sum s fun x : α => f x • g x :=
@@ -1275,7 +1275,7 @@ protected def domLCongr {α₁ α₂ : Type _} (e : α₁ ≃ α₂) : (α₁
lean 3 declaration is
forall {M : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {α₁ : Type.{u3}} {α₂ : Type.{u4}} (e : Equiv.{succ u3, succ u4} α₁ α₂) (v : Finsupp.{u3, u1} α₁ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))), Eq.{max (succ u4) (succ u1)} (Finsupp.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (coeFn.{max (succ (max u3 u1)) (succ (max u4 u1)), max (succ (max u3 u1)) (succ (max u4 u1))} (LinearEquiv.{u2, u2, max u3 u1, max u4 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (Finsupp.{u3, u1} α₁ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.addCommMonoid.{u3, u1} α₁ M _inst_3) (Finsupp.addCommMonoid.{u4, u1} α₂ M _inst_3) (Finsupp.module.{u3, u1, u2} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u1, u2} α₂ M R _inst_1 _inst_3 _inst_4)) (fun (_x : LinearEquiv.{u2, u2, max u3 u1, max u4 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (Finsupp.{u3, u1} α₁ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.addCommMonoid.{u3, u1} α₁ M _inst_3) (Finsupp.addCommMonoid.{u4, u1} α₂ M _inst_3) 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but is expected to have type
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α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u4 u2, max u3 u2} R R (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R 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(AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.add.{u4, u2} α₁ M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.add.{u3, u2} α₂ M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))))))) (Finsupp.domCongr.{u4, u3, u2} α₁ α₂ M _inst_3 e) v)
Case conversion may be inaccurate. Consider using '#align finsupp.dom_lcongr_apply Finsupp.domLCongr_applyₓ'. -/
@[simp]
theorem domLCongr_apply {α₁ : Type _} {α₂ : Type _} (e : α₁ ≃ α₂) (v : α₁ →₀ M) :
@@ -1322,7 +1322,7 @@ theorem domLCongr_symm {α₁ α₂ : Type _} (f : α₁ ≃ α₂) :
lean 3 declaration is
forall {M : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {α₁ : Type.{u3}} {α₂ : Type.{u4}} (e : Equiv.{succ u3, succ u4} α₁ α₂) (i : α₁) (m : M), Eq.{max (succ u4) (succ u1)} (Finsupp.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (coeFn.{max (succ (max u3 u1)) (succ (max u4 u1)), max (succ (max u3 u1)) (succ (max u4 u1))} (LinearEquiv.{u2, u2, max u3 u1, max u4 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (Finsupp.{u3, u1} α₁ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.addCommMonoid.{u3, u1} α₁ M _inst_3) (Finsupp.addCommMonoid.{u4, u1} α₂ M _inst_3) (Finsupp.module.{u3, u1, u2} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u1, u2} α₂ M R _inst_1 _inst_3 _inst_4)) (fun (_x : LinearEquiv.{u2, u2, max u3 u1, max u4 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (Finsupp.{u3, u1} α₁ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.addCommMonoid.{u3, u1} α₁ M _inst_3) (Finsupp.addCommMonoid.{u4, u1} α₂ M _inst_3) (Finsupp.module.{u3, u1, u2} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u1, u2} α₂ M R _inst_1 _inst_3 _inst_4)) => (Finsupp.{u3, u1} α₁ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) -> (Finsupp.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (LinearEquiv.hasCoeToFun.{u2, u2, max u3 u1, max u4 u1} R R (Finsupp.{u3, u1} α₁ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α₁ M _inst_3) (Finsupp.addCommMonoid.{u4, u1} α₂ M _inst_3) (Finsupp.module.{u3, u1, u2} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u1, u2} α₂ M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1)) (Finsupp.domLCongr.{u1, u2, u3, u4} M R _inst_1 _inst_3 _inst_4 α₁ α₂ e) (Finsupp.single.{u3, u1} α₁ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) i m)) (Finsupp.single.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (coeFn.{max 1 (max (succ u3) (succ u4)) (succ u4) (succ u3), max (succ u3) (succ u4)} (Equiv.{succ u3, succ u4} α₁ α₂) (fun (_x : Equiv.{succ u3, succ u4} α₁ α₂) => α₁ -> α₂) (Equiv.hasCoeToFun.{succ u3, succ u4} α₁ α₂) e i) m)
but is expected to have type
- forall {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {α₁ : Type.{u4}} {α₂ : Type.{u3}} (e : Equiv.{succ u4, succ u3} α₁ α₂) (i : α₁) (m : M), Eq.{max (succ u2) (succ u3)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.single.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) i m)) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u2), max (succ u3) (succ u2)} (LinearEquiv.{u1, u1, max u2 u4, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{u4, 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(Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (LinearEquiv.{u1, u1, max u2 u4, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4)) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u4 u2, max u3 u2, max (max u4 u3) u2} R R (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (LinearEquiv.{u1, u1, max u2 u4, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4)) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u4 u2, max u3 u2} R R (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1)))))) (Finsupp.domLCongr.{u2, u1, u4, u3} M R _inst_1 _inst_3 _inst_4 α₁ α₂ e) (Finsupp.single.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) i m)) (Finsupp.single.{u3, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α₁) => α₂) i) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Equiv.{succ u4, succ u3} α₁ α₂) α₁ (fun (_x : α₁) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α₁) => α₂) _x) (Equiv.instFunLikeEquiv.{succ u4, succ u3} α₁ α₂) e i) m)
+ forall {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {α₁ : Type.{u4}} {α₂ : Type.{u3}} (e : Equiv.{succ u4, succ u3} α₁ α₂) (i : α₁) (m : M), Eq.{max (succ u2) (succ u3)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.single.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) i m)) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u2), max (succ u3) (succ u2)} (LinearEquiv.{u1, u1, max u2 u4, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{u4, 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Case conversion may be inaccurate. Consider using '#align finsupp.dom_lcongr_single Finsupp.domLCongr_singleₓ'. -/
@[simp]
theorem domLCongr_single {α₁ : Type _} {α₂ : Type _} (e : α₁ ≃ α₂) (i : α₁) (m : M) :
@@ -1490,7 +1490,7 @@ def lcongr {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N) : (ι →
lean 3 declaration is
forall {M : Type.{u1}} {N : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : Module.{u3, u2} R N _inst_1 _inst_5] {ι : Type.{u4}} {κ : Type.{u5}} (e₁ : Equiv.{succ u4, succ u5} ι κ) (e₂ : LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (i : ι) (m : M), Eq.{max (succ u5) (succ u2)} (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) (coeFn.{max (succ (max u4 u1)) (succ (max u5 u2)), max (succ (max u4 u1)) (succ (max u5 u2))} (LinearEquiv.{u3, u3, max u4 u1, max u5 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) (Finsupp.addCommMonoid.{u4, u1} ι M _inst_3) (Finsupp.addCommMonoid.{u5, u2} κ N _inst_5) (Finsupp.module.{u4, u1, u3} ι M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u5, u2, u3} κ N R _inst_1 _inst_5 _inst_6)) (fun (_x : LinearEquiv.{u3, u3, max u4 u1, max u5 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) (Finsupp.addCommMonoid.{u4, u1} ι M _inst_3) (Finsupp.addCommMonoid.{u5, u2} κ N _inst_5) (Finsupp.module.{u4, u1, u3} ι M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u5, u2, u3} κ N R _inst_1 _inst_5 _inst_6)) => (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) -> (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))))) (LinearEquiv.hasCoeToFun.{u3, u3, max u4 u1, max u5 u2} R R (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u1} ι M _inst_3) (Finsupp.addCommMonoid.{u5, u2} κ N _inst_5) (Finsupp.module.{u4, u1, u3} ι M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u5, u2, u3} κ N R _inst_1 _inst_5 _inst_6) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)) (Finsupp.lcongr.{u1, u2, u3, u4, u5} M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 ι κ e₁ e₂) (Finsupp.single.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) i m)) (Finsupp.single.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))) (coeFn.{max 1 (max (succ u4) (succ u5)) (succ u5) (succ u4), max (succ u4) (succ u5)} (Equiv.{succ u4, succ u5} ι κ) (fun (_x : Equiv.{succ u4, succ u5} ι κ) => ι -> κ) (Equiv.hasCoeToFun.{succ u4, succ u5} ι κ) e₁ i) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (_x : LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) => M -> N) (LinearEquiv.hasCoeToFun.{u3, u3, u1, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)) e₂ m))
but is expected to have type
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u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) R M N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} M _inst_3) (AddCommMonoid.toAddMonoid.{u1} N _inst_5) (Module.toDistribMulAction.{u3, u2} R M _inst_1 _inst_3 _inst_4) (Module.toDistribMulAction.{u3, u1} R N _inst_1 _inst_5 _inst_6) (SemilinearMapClass.distribMulActionHomClass.{u3, u2, u1, max u2 u1} R M N (LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 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+ forall {M : Type.{u2}} {N : Type.{u1}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : Module.{u3, u1} R N _inst_1 _inst_5] {ι : Type.{u5}} {κ : Type.{u4}} (e₁ : Equiv.{succ u5, succ u4} ι κ) (e₂ : LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (i : ι) (m : M), Eq.{max (succ u1) (succ u4)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (Finsupp.single.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) i m)) 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(AddCommMonoid.toAddMonoid.{u1} N _inst_5))) _inst_1 (Finsupp.addCommMonoid.{u4, u1} κ N _inst_5) (Finsupp.module.{u4, u1, u3} κ N R _inst_1 _inst_5 _inst_6)) (SemilinearMapClass.distribMulActionHomClass.{u3, max u2 u5, max u1 u4, max (max (max u2 u1) u4) u5} R (Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (LinearEquiv.{u3, u3, max u2 u5, max u1 u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (Finsupp.addCommMonoid.{u5, u2} ι M _inst_3) (Finsupp.addCommMonoid.{u4, u1} κ N _inst_5) 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(Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (Finsupp.addCommMonoid.{u5, u2} ι M _inst_3) (Finsupp.addCommMonoid.{u4, u1} κ N _inst_5) (Finsupp.module.{u5, u2, u3} ι M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u1, u3} κ N R _inst_1 _inst_5 _inst_6)) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u5, u2} ι M _inst_3) (Finsupp.addCommMonoid.{u4, u1} κ N _inst_5) (Finsupp.module.{u5, u2, u3} ι M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u1, u3} κ N R _inst_1 _inst_5 _inst_6) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, max u2 u5, max u1 u4} R R (Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) 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(SMulZeroClass.toSMul.{u3, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (DistribSMul.toSMulZeroClass.{u3, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (DistribMulAction.toDistribSMul.{u3, u2} R M (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} M _inst_3) (Module.toDistribMulAction.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u3, u1} R N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5)) (DistribSMul.toSMulZeroClass.{u3, u1} R N (AddMonoid.toAddZeroClass.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5)) (DistribMulAction.toDistribSMul.{u3, u1} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_5) (Module.toDistribMulAction.{u3, u1} R N _inst_1 _inst_5 _inst_6)))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) R M N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} M _inst_3) (AddCommMonoid.toAddMonoid.{u1} N _inst_5) (Module.toDistribMulAction.{u3, u2} R M _inst_1 _inst_3 _inst_4) (Module.toDistribMulAction.{u3, u1} R N _inst_1 _inst_5 _inst_6) (SemilinearMapClass.distribMulActionHomClass.{u3, u2, u1, max u2 u1} R M N (LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 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Case conversion may be inaccurate. Consider using '#align finsupp.lcongr_single Finsupp.lcongr_singleₓ'. -/
@[simp]
theorem lcongr_single {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N) (i : ι) (m : M) :
@@ -1501,7 +1501,7 @@ theorem lcongr_single {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N)
lean 3 declaration is
forall {M : Type.{u1}} {N : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : Module.{u3, u2} R N _inst_1 _inst_5] {ι : Type.{u4}} {κ : Type.{u5}} (e₁ : Equiv.{succ u4, succ u5} ι κ) (e₂ : LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (f : Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (k : κ), Eq.{succ u2} N (coeFn.{max (succ u5) (succ u2), max (succ u5) (succ u2)} (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) (fun (_x : Finsupp.{u5, u2} κ N 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u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))))) (LinearEquiv.hasCoeToFun.{u3, u3, max u4 u1, max u5 u2} R R (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u1} ι M _inst_3) (Finsupp.addCommMonoid.{u5, u2} κ N _inst_5) (Finsupp.module.{u4, u1, u3} ι M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u5, u2, u3} κ N R _inst_1 _inst_5 _inst_6) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)) (Finsupp.lcongr.{u1, u2, u3, u4, u5} M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 ι κ e₁ e₂) f) k) (coeFn.{max (succ u1) (succ 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but is expected to have type
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+ forall {M : Type.{u2}} {N : Type.{u1}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : Module.{u3, u1} R N _inst_1 _inst_5] {ι : Type.{u5}} {κ : Type.{u4}} (e₁ : Equiv.{succ u5, succ u4} ι κ) (e₂ : LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (f : Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (k : κ), Eq.{succ u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : κ) => N) k) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) κ (fun (_x : κ) => (fun 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(Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, u2, u1} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)))))) e₂ (FunLike.coe.{max (succ u5) (succ u2), succ u5, succ u2} (Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => M) _x) (Finsupp.funLike.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) f (FunLike.coe.{max (succ u5) (succ u4), succ u4, succ u5} (Equiv.{succ u4, succ u5} κ ι) κ (fun (_x : κ) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : κ) => ι) _x) (Equiv.instFunLikeEquiv.{succ u4, succ u5} κ ι) (Equiv.symm.{succ u5, succ u4} ι κ e₁) k)))
Case conversion may be inaccurate. Consider using '#align finsupp.lcongr_apply_apply Finsupp.lcongr_apply_applyₓ'. -/
@[simp]
theorem lcongr_apply_apply {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N) (f : ι →₀ M) (k : κ) :
@@ -1513,7 +1513,7 @@ theorem lcongr_apply_apply {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[
lean 3 declaration is
forall {M : Type.{u1}} {N : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : Module.{u3, u2} R N _inst_1 _inst_5] {ι : Type.{u4}} {κ : Type.{u5}} (e₁ : Equiv.{succ u4, succ u5} ι κ) (e₂ : LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (k : κ) (n : N), Eq.{max (succ u4) (succ u1)} (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (coeFn.{max (succ (max u5 u2)) (succ (max u4 u1)), max (succ (max u5 u2)) (succ (max u4 u1))} (LinearEquiv.{u3, u3, max u5 u2, max u4 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R 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(AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.addCommMonoid.{u5, u2} κ N _inst_5) (Finsupp.addCommMonoid.{u4, u1} ι M _inst_3) (Finsupp.module.{u5, u2, u3} κ N R _inst_1 _inst_5 _inst_6) (Finsupp.module.{u4, u1, u3} ι M R _inst_1 _inst_3 _inst_4)) => (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) -> (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (LinearEquiv.hasCoeToFun.{u3, u3, max u5 u2, max u4 u1} R R (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u5, u2} κ N _inst_5) (Finsupp.addCommMonoid.{u4, u1} ι M _inst_3) (Finsupp.module.{u5, u2, u3} κ N R _inst_1 _inst_5 _inst_6) (Finsupp.module.{u4, u1, u3} ι M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)) (LinearEquiv.symm.{u3, u3, max u4 u1, max u5 u2} R R (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u1} ι M _inst_3) (Finsupp.addCommMonoid.{u5, u2} κ N _inst_5) (Finsupp.module.{u4, u1, u3} ι M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u5, u2, u3} κ N R _inst_1 _inst_5 _inst_6) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.lcongr.{u1, u2, u3, u4, u5} M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 ι κ e₁ e₂)) (Finsupp.single.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))) k n)) (Finsupp.single.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (coeFn.{max 1 (max (succ u5) (succ u4)) (succ u4) (succ u5), max (succ u5) (succ u4)} (Equiv.{succ u5, succ u4} κ ι) (fun (_x : Equiv.{succ u5, succ u4} κ ι) => κ -> ι) (Equiv.hasCoeToFun.{succ u5, succ u4} κ ι) (Equiv.symm.{succ u4, succ u5} ι κ e₁) k) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) N M _inst_5 _inst_3 _inst_6 _inst_4) (fun (_x : LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) N M _inst_5 _inst_3 _inst_6 _inst_4) => N -> M) (LinearEquiv.hasCoeToFun.{u3, u3, u2, u1} R R N M _inst_1 _inst_1 _inst_5 _inst_3 _inst_6 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)) (LinearEquiv.symm.{u3, u3, u1, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) e₂) n))
but is expected to have type
- forall {M : Type.{u2}} {N : Type.{u1}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : Module.{u3, u1} R N _inst_1 _inst_5] {ι : Type.{u5}} {κ : Type.{u4}} (e₁ : Equiv.{succ u5, succ u4} ι κ) (e₂ : LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (k : κ) (n : N), Eq.{max (succ u2) (succ u5)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) => Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.single.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5)) k n)) 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(x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) => Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _x) (SMulHomClass.toFunLike.{max (max (max u2 u1) u4) u5, u3, max u1 u4, max u2 u5} (LinearEquiv.{u3, u3, max u1 u4, max u2 u5} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u1} κ N _inst_5) (Finsupp.addCommMonoid.{u5, u2} ι M _inst_3) (Finsupp.module.{u4, u1, u3} κ N R _inst_1 _inst_5 _inst_6) (Finsupp.module.{u5, u2, u3} ι M R _inst_1 _inst_3 _inst_4)) R (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulZeroClass.toSMul.{u3, max u1 u4} R (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (AddMonoid.toZero.{max u1 u4} (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (Finsupp.addCommMonoid.{u4, u1} κ N _inst_5))) (DistribSMul.toSMulZeroClass.{u3, max u1 u4} R (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (AddMonoid.toAddZeroClass.{max u1 u4} (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) 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_inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u1} κ N _inst_5) (Finsupp.addCommMonoid.{u5, u2} ι M _inst_3) (Finsupp.module.{u4, u1, u3} κ N R _inst_1 _inst_5 _inst_6) (Finsupp.module.{u5, u2, u3} ι M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)))))) (LinearEquiv.symm.{u3, u3, max u2 u5, max u1 u4} R R (Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u5, u2} ι M _inst_3) (Finsupp.addCommMonoid.{u4, u1} κ N _inst_5) (Finsupp.module.{u5, u2, u3} ι M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u1, u3} κ N R _inst_1 _inst_5 _inst_6) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.lcongr.{u2, u1, u3, u5, u4} M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 ι κ e₁ e₂)) (Finsupp.single.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5)) k n)) (Finsupp.single.{u5, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : κ) => ι) k) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : N) => M) n) (AddMonoid.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : N) => M) n) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : N) => M) n) _inst_3)) (FunLike.coe.{max (succ u4) (succ u5), succ u4, succ u5} (Equiv.{succ u4, succ u5} κ ι) κ (fun (_x : κ) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : κ) => ι) _x) (Equiv.instFunLikeEquiv.{succ u4, succ u5} κ ι) (Equiv.symm.{succ u5, succ u4} ι κ e₁) k) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) N M _inst_5 _inst_3 _inst_6 _inst_4) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : N) => M) _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u1, u2} (LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) N M _inst_5 _inst_3 _inst_6 _inst_4) R N M (SMulZeroClass.toSMul.{u3, u1} R N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5)) (DistribSMul.toSMulZeroClass.{u3, u1} R N (AddMonoid.toAddZeroClass.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5)) (DistribMulAction.toDistribSMul.{u3, u1} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_5) (Module.toDistribMulAction.{u3, u1} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u3, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (DistribSMul.toSMulZeroClass.{u3, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (DistribMulAction.toDistribSMul.{u3, u2} R M (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} M _inst_3) (Module.toDistribMulAction.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u1, u2} (LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) N M _inst_5 _inst_3 _inst_6 _inst_4) R N M (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_5) (AddCommMonoid.toAddMonoid.{u2} M _inst_3) (Module.toDistribMulAction.{u3, u1} R N _inst_1 _inst_5 _inst_6) (Module.toDistribMulAction.{u3, u2} R M _inst_1 _inst_3 _inst_4) (SemilinearMapClass.distribMulActionHomClass.{u3, u1, u2, max u2 u1} R N M (LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) N M _inst_5 _inst_3 _inst_6 _inst_4) _inst_1 _inst_5 _inst_3 _inst_6 _inst_4 (SemilinearEquivClass.instSemilinearMapClass.{u3, u3, u1, u2, max u2 u1} R R N M (LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) N M _inst_5 _inst_3 _inst_6 _inst_4) _inst_1 _inst_1 _inst_5 _inst_3 _inst_6 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, u1, u2} R R N M _inst_1 _inst_1 _inst_5 _inst_3 _inst_6 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)))))) (LinearEquiv.symm.{u3, u3, u2, u1} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) e₂) n))
+ forall {M : Type.{u2}} {N : Type.{u1}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : Module.{u3, u1} R N _inst_1 _inst_5] {ι : Type.{u5}} {κ : Type.{u4}} (e₁ : Equiv.{succ u5, succ u4} ι κ) (e₂ : LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (k : κ) (n : N), Eq.{max (succ u2) (succ u5)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) => Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.single.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5)) k n)) 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(RingHomInvPair.ids.{u3} R _inst_1) N M _inst_5 _inst_3 _inst_6 _inst_4) _inst_1 _inst_1 _inst_5 _inst_3 _inst_6 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, u1, u2} R R N M _inst_1 _inst_1 _inst_5 _inst_3 _inst_6 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)))))) (LinearEquiv.symm.{u3, u3, u2, u1} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) e₂) n))
Case conversion may be inaccurate. Consider using '#align finsupp.lcongr_symm_single Finsupp.lcongr_symm_singleₓ'. -/
theorem lcongr_symm_single {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N) (k : κ) (n : N) :
(lcongr e₁ e₂).symm (Finsupp.single k n) = Finsupp.single (e₁.symm k) (e₂.symm n) :=
@@ -1749,7 +1749,7 @@ variable {S}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] {S : Type.{u4}} [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (f : α -> R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R 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(Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) f) (Finset.sum.{u2, u1} M α _inst_3 (Finset.univ.{u1} α _inst_1) (fun (i : α) => SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (f i) (v i)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (f : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> R) => M) f) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R 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(α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R 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(Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13959 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) f) (Finset.sum.{u4, u3} M α _inst_3 (Finset.univ.{u3} α _inst_1) (fun (i : α) => HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) (f i) (v i)))
+ forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (f : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) f) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearMap.{u1, u1, max u3 u4, max u4 u3 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u3, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14081 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14081 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14081 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) f) (Finset.sum.{u4, u3} M α _inst_3 (Finset.univ.{u3} α _inst_1) (fun (i : α) => HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) (f i) (v i)))
Case conversion may be inaccurate. Consider using '#align fintype.total_apply Fintype.total_applyₓ'. -/
theorem Fintype.total_apply (f) : Fintype.total R S v f = ∑ i, f i • v i :=
rfl
@@ -1759,7 +1759,7 @@ theorem Fintype.total_apply (f) : Fintype.total R S v f = ∑ i, f i • v i :=
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] {S : Type.{u4}} [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (i : α) (r : R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) => (α -> R) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (coeFn.{max (succ (max u1 u2)) (succ (max (max u1 u3) u2)), max (succ (max u1 u2)) (succ (max (max u1 u3) u2))} (LinearMap.{u4, u4, max u1 u2, max (max u1 u3) u2} S S _inst_5 _inst_5 (RingHom.id.{u4} S 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(Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) (fun (_x : LinearMap.{u4, u4, max u1 u2, max (max u1 u3) u2} S S _inst_5 _inst_5 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) => (α -> M) -> (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4)) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, max (max u1 u3) u2} S S (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) (Pi.single.{u1, u3} α (fun (ᾰ : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u1} α a b)) (fun (i : α) => MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) i r)) (SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) r (v i))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (i : α) (r : R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> R) => M) (Pi.single.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) v) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearMap.{u1, u1, max u3 u4, max u4 u3 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u3, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13959 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13959 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13959 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) (Pi.single.{u3, u2} α (fun (ᾰ : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) r (v i))
+ forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (i : α) (r : R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) (Pi.single.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) v) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearMap.{u1, u1, max u3 u4, max u4 u3 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u3, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14081 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14081 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14081 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) (Pi.single.{u3, u2} α (fun (ᾰ : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) r (v i))
Case conversion may be inaccurate. Consider using '#align fintype.total_apply_single Fintype.total_apply_singleₓ'. -/
@[simp]
theorem Fintype.total_apply_single (i : α) (r : R) :
@@ -1775,7 +1775,7 @@ variable (S)
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] (S : Type.{u4}) [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (x : α -> R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))) M _inst_2 _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Finsupp.total.{u1, u2, u3} α M R _inst_2 _inst_3 _inst_4 v) (coeFn.{succ (max u1 u3), succ (max u1 u3)} (LinearEquiv.{u3, u3, max u1 u3, max u1 u3} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHomInvPair.ids.{u3} R _inst_2) (RingHomInvPair.ids.{u3} R _inst_2) (α -> R) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R 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(Semiring.toModule.{u3} R _inst_2))) (fun (_x : LinearEquiv.{u3, u3, max u1 u3, max u1 u3} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHomInvPair.ids.{u3} R _inst_2) (RingHomInvPair.ids.{u3} R _inst_2) (α -> R) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))))) (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) 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(Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) x)
but is expected to have type
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(MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (x : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) => M) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (α -> R) (fun (a : α -> R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> R) => Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) a) (SMulHomClass.toFunLike.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (α -> R) (AddMonoid.toZero.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (α -> R) (AddMonoid.toAddZeroClass.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (α -> R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u3 u2, max u3 u2, max u3 u2} R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u3 u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u3 u2, max u3 u2, max u3 u2} R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} 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NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) v) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearMap.{u1, u1, max u3 u4, max u4 u3 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u3, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13959 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13959 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13959 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) x)
+ forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (x : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) => M) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (α -> R) (fun (a : α -> R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> R) => Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) a) (SMulHomClass.toFunLike.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (α -> R) (AddMonoid.toZero.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (α -> R) (AddMonoid.toAddZeroClass.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (α -> R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u3 u2, max u3 u2, max u3 u2} R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u3 u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α 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(AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 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R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u3 u2, max u3 u2, max u3 u2} R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} 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Case conversion may be inaccurate. Consider using '#align finsupp.total_eq_fintype_total_apply Finsupp.total_eq_fintype_total_applyₓ'. -/
theorem Finsupp.total_eq_fintype_total_apply (x : α → R) :
Finsupp.total α M R v ((Finsupp.linearEquivFunOnFinite R R α).symm x) = Fintype.total R S v x :=
@@ -1791,7 +1791,7 @@ theorem Finsupp.total_eq_fintype_total_apply (x : α → R) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] (S : Type.{u4}) [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (LinearMap.comp.{u3, u3, u3, max u1 u3, max u1 u3, u2} R R R (α -> R) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))) M _inst_2 _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHomCompTriple.right_ids.{u3, u3} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Finsupp.total.{u1, u2, u3} α M R _inst_2 _inst_3 _inst_4 v) (LinearEquiv.toLinearMap.{u3, u3, max u1 u3, max u1 u3} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHomInvPair.ids.{u3} R _inst_2) (RingHomInvPair.ids.{u3} R _inst_2) (α -> R) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))))) (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) (LinearEquiv.symm.{u3, u3, max u1 u3, max u1 u3} R R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))))) (α -> R) _inst_2 _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHomInvPair.ids.{u3} R _inst_2) (RingHomInvPair.ids.{u3} R _inst_2) (Finsupp.linearEquivFunOnFinite.{u3, u3, u1} R R α (Finite.of_fintype.{u1} α _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) _inst_2 (Semiring.toModule.{u3} R _inst_2))))) (coeFn.{max (succ (max u1 u2)) (succ (max (max u1 u3) u2)), max (succ (max u1 u2)) (succ (max (max u1 u3) u2))} (LinearMap.{u4, u4, max u1 u2, max (max u1 u3) u2} S S _inst_5 _inst_5 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4)) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, max (max u1 u3) u2} S S (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)
but is expected to have type
- forall {α : Type.{u4}} {M : Type.{u3}} (R : Type.{u2}) [_inst_1 : Fintype.{u4} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u3} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u3} R S M (SMulZeroClass.toSMul.{u2, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u2, u3} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u3} S M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u1, u3} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (LinearMap.comp.{u2, u2, u2, max u4 u2, max u4 u2, u3} R R R (α -> R) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) M _inst_2 _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomCompTriple.ids.{u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Finsupp.total.{u4, u3, u2} α M R _inst_2 _inst_3 _inst_4 v) (LinearEquiv.toLinearMap.{u2, u2, max u4 u2, max u4 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u4, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (LinearEquiv.symm.{u2, u2, max u4 u2, max u4 u2} R R (Finsupp.{u4, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (α -> R) _inst_2 _inst_2 (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (Finsupp.linearEquivFunOnFinite.{u2, u2, u4} R R α (Finite.of_fintype.{u4} α _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) _inst_2 (Semiring.toModule.{u2} R _inst_2))))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), max (max (succ u2) (succ u3)) (succ u4)} (LinearMap.{u1, u1, max u4 u3, max u3 u4 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u4, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13959 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u4 u2, u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u4, u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13959 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u4 u2, u3} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u4, max (max u2 u3) u4} S S (α -> M) (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u4, u3} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u4 u2, u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u4, u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13959 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u4 u2, u3} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u4, u3, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)
+ forall {α : Type.{u4}} {M : Type.{u3}} (R : Type.{u2}) [_inst_1 : Fintype.{u4} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u3} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u3} R S M (SMulZeroClass.toSMul.{u2, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u2, u3} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u3} S M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u1, u3} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (LinearMap.comp.{u2, u2, u2, max u4 u2, max u4 u2, u3} R R R (α -> R) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) M _inst_2 _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.429 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomCompTriple.ids.{u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Finsupp.total.{u4, u3, u2} α M R _inst_2 _inst_3 _inst_4 v) (LinearEquiv.toLinearMap.{u2, u2, max u4 u2, max u4 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u4, u2} α R (AddMonoid.toZero.{u2} R 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_inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u4, u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14081 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u4 u2, u3} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u4, u3, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)
Case conversion may be inaccurate. Consider using '#align finsupp.total_eq_fintype_total Finsupp.total_eq_fintype_totalₓ'. -/
theorem Finsupp.total_eq_fintype_total :
(Finsupp.total α M R v).comp (Finsupp.linearEquivFunOnFinite R R α).symm.toLinearMap =
@@ -1805,7 +1805,7 @@ variable {S}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] {S : Type.{u4}} [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{succ u2} (Submodule.{u3, u2} R M _inst_2 _inst_3 _inst_4) (LinearMap.range.{u3, u3, max u1 u3, u2, max (max u1 u3) u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (LinearMap.semilinearMapClass.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (RingHomSurjective.ids.{u3} R _inst_2) (coeFn.{max (succ (max u1 u2)) (succ (max (max u1 u3) u2)), max (succ (max u1 u2)) (succ (max (max u1 u3) u2))} (LinearMap.{u4, u4, max u1 u2, max (max u1 u3) u2} S S _inst_5 _inst_5 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) (fun (_x : LinearMap.{u4, u4, max u1 u2, max (max u1 u3) u2} S S _inst_5 _inst_5 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) => (α -> M) -> (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4)) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, max (max u1 u3) u2} S S (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)) (Submodule.span.{u3, u2} R M _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u1} M α v))
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u4}} (R : Type.{u3}) [_inst_1 : Fintype.{u2} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u3, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u1, u4} R S M (SMulZeroClass.toSMul.{u3, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u4} R M (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u4} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u3, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{succ u4} (Submodule.{u3, u4} R M _inst_2 _inst_3 _inst_4) (LinearMap.range.{u3, u3, max u2 u3, u4, max (max u2 u4) u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) v) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (RingHomSurjective.ids.{u3} R _inst_2) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearMap.{u1, u1, max u2 u4, max u4 u2 u3} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u2, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13959 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun 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(Pi.module.{u2, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13959 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u2 u3, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u2, u4, u3, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)) (Submodule.span.{u3, u4} R M _inst_2 _inst_3 _inst_4 (Set.range.{u4, succ u2} M α v))
+ forall {α : Type.{u2}} {M : Type.{u4}} (R : Type.{u3}) [_inst_1 : Fintype.{u2} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u3, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u1, u4} R S M (SMulZeroClass.toSMul.{u3, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u4} R M (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u4} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u3, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{succ u4} (Submodule.{u3, u4} R M _inst_2 _inst_3 _inst_4) (LinearMap.range.{u3, u3, max u2 u3, u4, max (max u2 u4) u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) v) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (RingHomSurjective.ids.{u3} R _inst_2) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearMap.{u1, u1, max u2 u4, max u4 u2 u3} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u2, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14081 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun 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NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> M) => LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14093 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R 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_inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)) (Submodule.span.{u3, u4} R M _inst_2 _inst_3 _inst_4 (Set.range.{u4, succ u2} M α v))
Case conversion may be inaccurate. Consider using '#align fintype.range_total Fintype.range_totalₓ'. -/
@[simp]
theorem Fintype.range_total : (Fintype.total R S v).range = Submodule.span R (Set.range v) := by
@@ -1877,7 +1877,7 @@ irreducible_def Span.repr (w : Set M) (x : span R w) : w →₀ R :=
lean 3 declaration is
forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {w : Set.{u2} M} (x : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w)), Eq.{succ u2} M (coeFn.{max (succ (max u2 u1)) (succ u2), max (succ (max u2 u1)) (succ u2)} (LinearMap.{u1, u1, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) w) R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (Finsupp.addCommMonoid.{u2, u1} 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_inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w)) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w)))))) x)
but is expected to have type
- forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {w : Set.{u2} M} (x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) (Span.repr.{u1, u2} R M _inst_1 _inst_2 _inst_3 w x)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} (Set.Elem.{u2} M w) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} (Set.Elem.{u2} M w) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) (Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u2} R R (Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} (Set.Elem.{u2} M w) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} (Set.Elem.{u2} M w) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} (Set.Elem.{u2} M w) M R _inst_1 _inst_2 _inst_3 (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x w))) (Span.repr.{u1, u2} R M _inst_1 _inst_2 _inst_3 w x)) (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w))) x)
+ forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {w : Set.{u2} M} (x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) (Span.repr.{u1, u2} R M _inst_1 _inst_2 _inst_3 w x)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} (Set.Elem.{u2} M w) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} (Set.Elem.{u2} M w) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) (Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u2} R R (Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} (Set.Elem.{u2} M w) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} (Set.Elem.{u2} M w) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} (Set.Elem.{u2} M w) M R _inst_1 _inst_2 _inst_3 (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x w))) (Span.repr.{u1, u2} R M _inst_1 _inst_2 _inst_3 w x)) (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w))) x)
Case conversion may be inaccurate. Consider using '#align span.finsupp_total_repr Span.finsupp_total_reprₓ'. -/
@[simp]
theorem Span.finsupp_total_repr {w : Set M} (x : span R w) :
@@ -1904,7 +1904,7 @@ protected theorem Submodule.finsupp_sum_mem {ι β : Type _} [Zero β] (S : Subm
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_4] (f : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M N _inst_2 _inst_4 _inst_3 _inst_5) {ι : Type.{u4}} {g : ι -> M} (l : Finsupp.{u4, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))), Eq.{succ u3} N (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M N _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M N _inst_2 _inst_4 _inst_3 _inst_5) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M N _inst_1 _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u4, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (Finsupp.addCommMonoid.{u4, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u4, u1, u1} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u4, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (Finsupp.addCommMonoid.{u4, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u4, u1, u1} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) => (Finsupp.{u4, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} R R (Finsupp.{u4, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u4, u1, u1} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u4, u2, u1} ι M R _inst_1 _inst_2 _inst_3 g) l)) (coeFn.{max (succ (max u4 u1)) (succ u3), max (succ (max u4 u1)) (succ u3)} (LinearMap.{u1, u1, max u4 u1, 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(x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u4 u1, u3} R R (Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u4, u4} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Finsupp.total.{u1, u3, u4} ι M R _inst_1 _inst_2 _inst_3 g) l)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u1), max (succ u4) (succ u1), succ u2} (LinearMap.{u4, u4, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) N (Finsupp.addCommMonoid.{u1, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_4 (Finsupp.module.{u1, u4, u4} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_5) (Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) (fun (_x : Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u4 u1, u2} R R (Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_4 (Finsupp.module.{u1, u4, u4} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Finsupp.total.{u1, u2, u4} ι N R _inst_1 _inst_4 _inst_5 (Function.comp.{succ u1, succ u3, succ u2} ι M N (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (LinearMap.{u4, u4, u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_2 _inst_4 _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, u2} R R M N _inst_1 _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) f) g)) l)
Case conversion may be inaccurate. Consider using '#align linear_map.map_finsupp_total LinearMap.map_finsupp_totalₓ'. -/
theorem LinearMap.map_finsupp_total (f : M →ₗ[R] N) {ι : Type _} {g : ι → M} (l : ι →₀ R) :
f (Finsupp.total ι M R g l) = Finsupp.total ι N R (f ∘ g) l := by
@@ -2004,7 +2004,7 @@ open Finsupp Function
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_1 _inst_1 _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3)
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} (f : LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u1) (succ u3)} M (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u3} R R M (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _inst_1 _inst_1 _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} (f : LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u1) (succ u3)} M (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u3} R R M (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _inst_1 _inst_1 _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3)
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_finsupp_surjective LinearMap.splittingOfFinsuppSurjectiveₓ'. -/
-- See also `linear_map.splitting_of_fun_on_fintype_surjective`
/-- A surjective linear map to finitely supported functions has a splitting. -/
@@ -2016,7 +2016,7 @@ def splittingOfFinsuppSurjective (f : M →ₗ[R] α →₀ R) (s : Surjective f
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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but is expected to have type
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (LinearMap.comp.{u3, u3, u3, max u3 u1, u2, max u3 u1} R R R (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} 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+ forall {R : Type.{u3}} {M : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u3, u2} R M _inst_1 _inst_2] {α : Type.{u1}} (f : LinearMap.{u3, u3, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (FunLike.coe.{max 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(MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_1 _inst_1 _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)), Eq.{max (succ u3) (succ u1)} (LinearMap.{u3, u3, max u3 u1, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (LinearMap.comp.{u3, u3, u3, max u3 u1, u2, max u3 u1} R R R (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomCompTriple.ids.{u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f (LinearMap.splittingOfFinsuppSurjective.{u3, u2, u1} R M _inst_1 _inst_2 _inst_3 α f s)) (LinearMap.id.{u3, max u3 u1} R (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)))
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_finsupp_surjective_splits LinearMap.splittingOfFinsuppSurjective_splitsₓ'. -/
theorem splittingOfFinsuppSurjective_splits (f : M →ₗ[R] α →₀ R) (s : Surjective f) :
f.comp (splittingOfFinsuppSurjective f s) = LinearMap.id :=
@@ -2033,7 +2033,7 @@ theorem splittingOfFinsuppSurjective_splits (f : M →ₗ[R] α →₀ R) (s : S
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M 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_inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_1 _inst_1 _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Function.LeftInverse.{max (succ u3) (succ u1), succ u2} (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 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but is expected to have type
- forall {R : Type.{u3}} {M : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u3, u2} R M _inst_1 _inst_2] {α : Type.{u1}} (f : LinearMap.{u3, u3, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (FunLike.coe.{max 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+ forall {R : Type.{u3}} {M : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u3, u2} R M _inst_1 _inst_2] {α : Type.{u1}} (f : LinearMap.{u3, u3, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (FunLike.coe.{max 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(MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_1 _inst_1 _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)), Function.LeftInverse.{max (succ u3) (succ u1), succ u2} (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u2, max (succ u3) (succ u1)} (LinearMap.{u3, u3, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u3} α R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.splittingOfFinsuppSurjective.{u3, u2, u1} R M _inst_1 _inst_2 _inst_3 α f s))
Case conversion may be inaccurate. Consider using '#align linear_map.left_inverse_splitting_of_finsupp_surjective LinearMap.leftInverse_splittingOfFinsuppSurjectiveₓ'. -/
theorem leftInverse_splittingOfFinsuppSurjective (f : M →ₗ[R] α →₀ R) (s : Surjective f) :
LeftInverse f (splittingOfFinsuppSurjective f s) := fun g =>
@@ -2044,7 +2044,7 @@ theorem leftInverse_splittingOfFinsuppSurjective (f : M →ₗ[R] α →₀ R) (
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M 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(Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_1 _inst_1 _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Function.Injective.{max (succ u3) (succ u1), succ u2} (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R 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(MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.splittingOfFinsuppSurjective.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 α f s))
but is expected to have type
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+ forall {R : Type.{u3}} {M : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u3, u2} R M _inst_1 _inst_2] {α : Type.{u1}} (f : LinearMap.{u3, u3, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u2, max (succ u3) (succ u1)} (LinearMap.{u3, u3, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, max u3 u1} R R M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_1 _inst_1 _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)), Function.Injective.{max (succ u3) (succ u1), succ u2} (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u1), succ u2} (LinearMap.{u3, u3, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_3) (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (fun (_x : Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u1, u2} R R (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.splittingOfFinsuppSurjective.{u3, u2, u1} R M _inst_1 _inst_2 _inst_3 α f s))
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_finsupp_surjective_injective LinearMap.splittingOfFinsuppSurjective_injectiveₓ'. -/
theorem splittingOfFinsuppSurjective_injective (f : M →ₗ[R] α →₀ R) (s : Surjective f) :
Injective (splittingOfFinsuppSurjective f s) :=
@@ -2055,7 +2055,7 @@ theorem splittingOfFinsuppSurjective_injective (f : M →ₗ[R] α →₀ R) (s
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3)
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16528 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u1) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16528 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16528 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16528 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16542 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) _inst_3)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16682 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u1) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16682 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16682 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16682 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16697 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) _inst_3)
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective LinearMap.splittingOfFunOnFintypeSurjectiveₓ'. -/
-- See also `linear_map.splitting_of_finsupp_surjective`
/-- A surjective linear map to functions on a finite type has a splitting. -/
@@ -2069,7 +2069,7 @@ def splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R) (s
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Eq.{succ (max u3 u1)} (LinearMap.{u1, u1, max u3 u1, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (LinearMap.comp.{u1, u1, u1, max u3 u1, u2, max u3 u1} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomCompTriple.right_ids.{u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u1, max u3 u1} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16608 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16608 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16608 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16608 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Eq.{max (succ u2) (succ u3)} (LinearMap.{u2, u2, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16542 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16608 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.comp.{u2, u2, u2, max u2 u3, u1, max u2 u3} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16542 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16608 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u2, max u2 u3} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16542 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16765 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16765 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16765 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16765 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Eq.{max (succ u2) (succ u3)} (LinearMap.{u2, u2, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16697 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16765 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.comp.{u2, u2, u2, max u2 u3, u1, max u2 u3} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16697 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16765 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u2, max u2 u3} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16697 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)))
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective_splits LinearMap.splittingOfFunOnFintypeSurjective_splitsₓ'. -/
theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : f.comp (splittingOfFunOnFintypeSurjective f s) = LinearMap.id :=
@@ -2085,7 +2085,7 @@ theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R]
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Function.LeftInverse.{max (succ u3) (succ u1), succ u2} (α -> R) M (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f) (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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but is expected to have type
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16542 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16542 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => 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+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16897 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), 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Case conversion may be inaccurate. Consider using '#align linear_map.left_inverse_splitting_of_fun_on_fintype_surjective LinearMap.leftInverse_splittingOfFunOnFintypeSurjectiveₓ'. -/
theorem leftInverse_splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : LeftInverse f (splittingOfFunOnFintypeSurjective f s) := fun g =>
@@ -2096,7 +2096,7 @@ theorem leftInverse_splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Function.Injective.{max (succ u3) (succ u1), succ u2} (α -> R) M (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) (fun (_x : LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) => (α -> R) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, u2} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16794 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16794 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16794 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16794 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Function.Injective.{max (succ u2) (succ u3), succ u1} (α -> R) M (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16542 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16542 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16542 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16956 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16956 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16956 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16956 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Function.Injective.{max (succ u2) (succ u3), succ u1} (α -> R) M (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16697 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16697 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16697 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective_injective LinearMap.splittingOfFunOnFintypeSurjective_injectiveₓ'. -/
theorem splittingOfFunOnFintypeSurjective_injective [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : Injective (splittingOfFunOnFintypeSurjective f s) :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/38f16f960f5006c6c0c2bac7b0aba5273188f4e5
@@ -576,7 +576,7 @@ variable (S) [Module S N] [SMulCommClass R S N]
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toHasSmul.{u4, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u4, u3} R N (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u5, u3} S N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u5, u3} S N (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))], LinearEquiv.{u5, u5, max u1 u2 u3, max (max u1 u2) u3} S S _inst_2 _inst_2 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2) (α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u1, max u2 u3} α (fun (ᾰ : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.Function.module.{u1, u5, max u2 u3} α S (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.module.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.module.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)
but is expected to have type
- forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toSMul.{u4, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u4, u3} R N (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u5, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} S N (MonoidWithZero.toZero.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))], LinearEquiv.{u5, u5, max (max u1 u2) u3, max u3 u2 u1} S S _inst_2 _inst_2 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2) (α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u4, u4, max u2 u1, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u1, max u2 u3} α (fun (ᾰ : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.module.{u1, max u2 u3, u5} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)
+ forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toSMul.{u4, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u4, u3} R N (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u5, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} S N (MonoidWithZero.toZero.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))], LinearEquiv.{u5, u5, max (max u1 u2) u3, max u3 u2 u1} S S _inst_2 _inst_2 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2) (α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u4, u4, max u2 u1, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u1, max u2 u3} α (fun (ᾰ : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.module.{u1, max u2 u3, u5} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)
Case conversion may be inaccurate. Consider using '#align finsupp.lsum Finsupp.lsumₓ'. -/
/-- Lift a family of linear maps `M →ₗ[R] N` indexed by `x : α` to a linear map from `α →₀ M` to
`N` using `finsupp.sum`. This is an upgraded version of `finsupp.lift_add_hom`.
@@ -608,7 +608,7 @@ def lsum : (α → M →ₗ[R] N) ≃ₗ[S] (α →₀ M) →ₗ[R] N
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toHasSmul.{u4, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u4, u3} R N (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u5, u3} S N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u5, u3} S N (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)), Eq.{max (max (succ u1) (succ u2)) (succ u3)} ((fun (_x : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) => (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) -> N) (coeFn.{max (succ (max u1 u2 u3)) (succ (max (max u1 u2) u3)), max (succ (max u1 u2 u3)) (succ (max (max u1 u2) u3))} (LinearEquiv.{u5, u5, max u1 u2 u3, max (max u1 u2) u3} S S _inst_2 _inst_2 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S 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_inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6)) (LinearEquiv.hasCoeToFun.{u5, u5, max u1 u2 u3, max (max u1 u2) u3} S S (α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u1, max u2 u3} α (fun (ᾰ : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.Function.module.{u1, u5, max u2 u3} α S (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.module.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.module.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2)) (Finsupp.lsum.{u1, u2, u3, u4, u5} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f)) (fun (d : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) => Finsupp.sum.{u1, u2, u3} α M N (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_5 d (fun (i : α) => coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (_x : LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) => M -> N) (LinearMap.hasCoeToFun.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (f i)))
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u4}} {N : Type.{u3}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u3} R S N (SMulZeroClass.toSMul.{u5, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)), Eq.{max (max (succ u2) (succ u4)) (succ u3)} (forall (a : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) a) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) 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(LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R 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_inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M 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(LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2} S S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f)) (fun (d : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => Finsupp.sum.{u2, u4, u3} α M ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) d) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) _inst_5 d (fun (i : α) => FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f i)))
+ forall {α : Type.{u2}} {M : Type.{u4}} {N : Type.{u3}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u3} R S N (SMulZeroClass.toSMul.{u5, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)), Eq.{max (max (succ u2) (succ u4)) (succ u3)} (forall (a : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) a) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) f) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (fun (_x : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (fun (_x : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _x) (SMulHomClass.toFunLike.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M 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(RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f)) (fun (d : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => Finsupp.sum.{u2, u4, u3} α M ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) d) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) _inst_5 d (fun (i : α) => FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f i)))
Case conversion may be inaccurate. Consider using '#align finsupp.coe_lsum Finsupp.coe_lsumₓ'. -/
@[simp]
theorem coe_lsum (f : α → M →ₗ[R] N) : (lsum S f : (α →₀ M) → N) = fun d => d.Sum fun i => f i :=
@@ -619,7 +619,7 @@ theorem coe_lsum (f : α → M →ₗ[R] N) : (lsum S f : (α →₀ M) → N) =
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toHasSmul.{u4, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u4, u3} R N (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u5, u3} S N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u5, u3} S N (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (l : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))), Eq.{succ u3} N (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (fun (_x : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 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_inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u1, max u2 u3} α (fun (ᾰ : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.Function.module.{u1, u5, max u2 u3} α S (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.module.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.module.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2)) (Finsupp.lsum.{u1, u2, u3, u4, u5} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f) l) (Finsupp.sum.{u1, u2, u3} α M N (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_5 l (fun (b : α) => coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (_x : LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) => M -> N) (LinearMap.hasCoeToFun.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (f b)))
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u4}} {N : Type.{u3}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u3} R S N (SMulZeroClass.toSMul.{u5, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (l : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) l) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), succ u3} ((fun 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_inst_2 _inst_9 _inst_10)) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (fun (_x : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _x) (SMulHomClass.toFunLike.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} 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_inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M 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(AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2} S S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f) l) (Finsupp.sum.{u2, u4, u3} α M N (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) _inst_5 l (fun (b : α) => FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f b)))
+ forall {α : Type.{u2}} {M : Type.{u4}} {N : Type.{u3}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u3} R S N (SMulZeroClass.toSMul.{u5, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (l : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) l) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) f) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (fun (_x : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (fun (_x : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _x) (SMulHomClass.toFunLike.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} 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_inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R 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(RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f) l) (Finsupp.sum.{u2, u4, u3} α M N (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) _inst_5 l (fun (b : α) => FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f b)))
Case conversion may be inaccurate. Consider using '#align finsupp.lsum_apply Finsupp.lsum_applyₓ'. -/
theorem lsum_apply (f : α → M →ₗ[R] N) (l : α →₀ M) : Finsupp.lsum S f l = l.Sum fun b => f b :=
rfl
@@ -629,7 +629,7 @@ theorem lsum_apply (f : α → M →ₗ[R] N) (l : α →₀ M) : Finsupp.lsum S
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toHasSmul.{u4, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u4, u3} R N (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u5, u3} S N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u5, u3} S N (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N 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(AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (i : α) (m : M), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) (Finsupp.single.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) i m)) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), succ u3} 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_inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => 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(Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 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(AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 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R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2} S S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f) (Finsupp.single.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) i m)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f i) m)
+ forall {α : Type.{u2}} {M : Type.{u4}} {N : Type.{u3}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u3} R S N (SMulZeroClass.toSMul.{u5, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (i : α) (m : M), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) (Finsupp.single.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) i m)) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) f) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (fun (_x : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (fun (_x : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _x) (SMulHomClass.toFunLike.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M 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(RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M 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u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) 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_inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2} S S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f) (Finsupp.single.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) i m)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f i) m)
Case conversion may be inaccurate. Consider using '#align finsupp.lsum_single Finsupp.lsum_singleₓ'. -/
theorem lsum_single (f : α → M →ₗ[R] N) (i : α) (m : M) :
Finsupp.lsum S f (Finsupp.single i m) = f i m :=
@@ -640,7 +640,7 @@ theorem lsum_single (f : α → M →ₗ[R] N) (i : α) (m : M) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toHasSmul.{u4, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u4, u3} R N (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u5, u3} S N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u5, u3} S N (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))] (f : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (x : α), Eq.{max (succ u2) (succ u3)} (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (coeFn.{max (succ (max (max u1 u2) u3)) (succ (max u1 u2 u3)), max (succ (max (max u1 u2) u3)) (succ (max u1 u2 u3))} (LinearEquiv.{u5, u5, max (max u1 u2) u3, max u1 u2 u3} S S _inst_2 _inst_2 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2) (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M 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(AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.Function.module.{u1, u5, max u2 u3} α S (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.module.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.module.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2) (Finsupp.lsum.{u1, u2, u3, u4, u5} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10)) f x) (LinearMap.comp.{u4, u4, u4, u2, max u1 u2, u3} R R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 _inst_4 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomCompTriple.right_ids.{u4, u4} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) f (Finsupp.lsingle.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4 x))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u4}} {N : Type.{u2}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : Module.{u5, u2} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u2} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u2} R S N (SMulZeroClass.toSMul.{u5, u2} R N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u2} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u2} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (Module.toMulActionWithZero.{u5, u2} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u2} S N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u2} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u2} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (Module.toMulActionWithZero.{u1, u2} S N _inst_2 _inst_5 _inst_9))))] (f : LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (x : α), Eq.{max (succ u4) (succ u2)} (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (max (succ u2) (succ u4)) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (fun (_x : LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) => α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _x) (SMulHomClass.toFunLike.{max (max u2 u4) u3, u1, max (max u2 u4) u3, max (max u2 u4) u3} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (SMulZeroClass.toSMul.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (SMulZeroClass.toSMul.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u4) u3, u1, max (max u2 u4) u3, max (max u2 u4) u3} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u2 u4) u3, max (max u2 u4) u3, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3, max (max u2 u4) u3} S S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) _inst_2 _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (LinearEquiv.symm.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (ᾰ : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (Finsupp.lsum.{u3, u4, u2, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10)) f x) (LinearMap.comp.{u5, u5, u5, u4, max u3 u4, u2} R R R M (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 _inst_4 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHomCompTriple.ids.{u5, u5} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) f (Finsupp.lsingle.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4 x))
+ forall {α : Type.{u3}} {M : Type.{u4}} {N : Type.{u2}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : Module.{u5, u2} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u2} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u2} R S N (SMulZeroClass.toSMul.{u5, u2} R N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u2} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u2} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (Module.toMulActionWithZero.{u5, u2} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u2} S N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u2} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u2} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (Module.toMulActionWithZero.{u1, u2} S N _inst_2 _inst_5 _inst_9))))] (f : LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (x : α), Eq.{max (succ u4) (succ u2)} (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (max (succ u2) (succ u4)) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (fun (_x : LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) => α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _x) (SMulHomClass.toFunLike.{max (max u2 u4) u3, u1, max (max u2 u4) u3, max (max u2 u4) u3} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (SMulZeroClass.toSMul.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (SMulZeroClass.toSMul.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u4) u3, u1, max (max u2 u4) u3, max (max u2 u4) u3} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u2 u4) u3, max (max u2 u4) u3, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R 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_inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M 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(Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (LinearEquiv.symm.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (ᾰ : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 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(RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (Finsupp.lsum.{u3, u4, u2, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10)) f x) (LinearMap.comp.{u5, u5, u5, u4, max u3 u4, u2} R R R M (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 _inst_4 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHomCompTriple.ids.{u5, u5} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) f (Finsupp.lsingle.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4 x))
Case conversion may be inaccurate. Consider using '#align finsupp.lsum_symm_apply Finsupp.lsum_symm_applyₓ'. -/
theorem lsum_symm_apply (f : (α →₀ M) →ₗ[R] N) (x : α) : (lsum S).symm f x = f.comp (lsingle x) :=
rfl
@@ -670,7 +670,7 @@ noncomputable def lift : (X → M) ≃+ ((X →₀ R) →ₗ[R] M) :=
lean 3 declaration is
forall (M : Type.{u1}) (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u3}) (f : LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (x : X), Eq.{succ u1} M (coeFn.{max (succ (max (max u3 u2) u1)) (succ 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(NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.instAdd.{u3, u1} X (fun (ᾰ : X) => M) (fun (i : X) => AddZeroClass.toHasAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (fun (_x : AddEquiv.{max (max u3 u2) u1, max u3 u1} (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (X -> M) (LinearMap.hasAdd.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.instAdd.{u3, u1} X (fun (ᾰ : X) => M) (fun (i : X) => AddZeroClass.toHasAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) => (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) -> X -> M) (AddEquiv.hasCoeToFun.{max (max u3 u2) u1, max u3 u1} (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (X -> M) (LinearMap.hasAdd.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.instAdd.{u3, u1} X (fun (ᾰ : X) => M) (fun (i : X) => AddZeroClass.toHasAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (AddEquiv.symm.{max u3 u1, max (max u3 u2) u1} (X -> M) (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (ᾰ : X) => M) (fun (i : X) => AddZeroClass.toHasAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.hasAdd.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.lift.{u1, u2, u3} M R _inst_1 _inst_3 _inst_4 X)) f x) (coeFn.{max (succ (max u3 u2)) (succ u1), max (succ (max u3 u2)) (succ u1)} (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) => (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f (Finsupp.single.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) x (OfNat.ofNat.{u2} R 1 (OfNat.mk.{u2} R 1 (One.one.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))))))
but is expected to have type
- forall (M : Type.{u1}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_3] (X : Type.{u2}) (f : LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (x : X), Eq.{succ u1} M (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2)} (AddEquiv.{max (max u1 u3) u2, max u1 u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (LinearMap.instAddLinearMap.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.instAdd.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => X -> M) _x) (AddHomClass.toFunLike.{max (max u1 u3) u2, max (max u1 u3) u2, max u1 u2} (AddEquiv.{max (max u1 u3) u2, max u1 u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (LinearMap.instAddLinearMap.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.instAdd.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (AddZeroClass.toAdd.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddMonoid.toAddZeroClass.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (AddZeroClass.toAdd.{max u1 u2} (X -> M) (Pi.addZeroClass.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (AddMonoidHomClass.toAddHomClass.{max (max u1 u3) u2, max (max u1 u3) u2, max u1 u2} (AddEquiv.{max (max u1 u3) u2, max u1 u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (LinearMap.instAddLinearMap.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.instAdd.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (AddMonoid.toAddZeroClass.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Pi.addZeroClass.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddEquivClass.instAddMonoidHomClass.{max (max u1 u3) u2, max (max u1 u3) u2, max u1 u2} (AddEquiv.{max (max u1 u3) u2, max u1 u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (LinearMap.instAddLinearMap.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.instAdd.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (AddMonoid.toAddZeroClass.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Pi.addZeroClass.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddEquiv.instAddEquivClassAddEquiv.{max (max u1 u3) u2, max u1 u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (LinearMap.instAddLinearMap.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.instAdd.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))) (AddEquiv.symm.{max u1 u2, max (max u1 u3) u2} (X -> M) (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lift.{u1, u3, u2} M R _inst_1 _inst_3 _inst_4 X)) f x) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R 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+ forall (M : Type.{u1}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_3] (X : Type.{u2}) (f : LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (x : X), Eq.{succ u1} M (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2)} (AddEquiv.{max (max u1 u3) u2, 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u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (LinearMap.instAddLinearMap.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.instAdd.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4916 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (AddZeroClass.toAdd.{max (max u1 u3) u2} (LinearMap.{u3, 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R 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Case conversion may be inaccurate. Consider using '#align finsupp.lift_symm_apply Finsupp.lift_symm_applyₓ'. -/
@[simp]
theorem lift_symm_apply (f) (x) : ((lift M R X).symm f) x = f (single x 1) :=
@@ -681,7 +681,7 @@ theorem lift_symm_apply (f) (x) : ((lift M R X).symm f) x = f (single x 1) :=
lean 3 declaration is
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(Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) 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(NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) => (X -> M) -> (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R 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(Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (ᾰ : X) => M) (fun (i : X) => AddZeroClass.toHasAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.hasAdd.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.lift.{u1, u2, u3} M R _inst_1 _inst_3 _inst_4 X) f) g) (Finsupp.sum.{u3, u2, u1} X R M (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 g (fun (x : X) (r : R) => SMul.smul.{u2, u1} R M (SMulZeroClass.toHasSmul.{u2, u1} R M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u1} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4)))) r (f x)))
but is expected to have type
- forall (M : Type.{u1}) (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u3}) (f : X -> M) (g : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) g) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : X -> M) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) f) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (max (succ u1) (succ u2)) (succ u3)} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R 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(Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (fun (_x : X -> M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : X -> M) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) _x) (AddHomClass.toFunLike.{max (max u1 u2) u3, max u1 u3, max (max u1 u2) u3} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddZeroClass.toAdd.{max u1 u3} (X -> M) (Pi.addZeroClass.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (AddZeroClass.toAdd.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (AddMonoidHomClass.toAddHomClass.{max (max u1 u2) u3, max u1 u3, max (max u1 u2) u3} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.addZeroClass.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddEquivClass.instAddMonoidHomClass.{max (max u1 u2) u3, max u1 u3, max (max u1 u2) u3} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.addZeroClass.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddEquiv.instAddEquivClassAddEquiv.{max u1 u3, max (max u1 u2) u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (Finsupp.lift.{u1, u2, u3} M R _inst_1 _inst_3 _inst_4 X) f) g) (Finsupp.sum.{u3, u2, u1} X R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) _inst_3 g (fun (x : X) (r : R) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4))))) r (f x)))
+ forall (M : Type.{u1}) (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u3}) (f : X -> M) (g : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) g) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : X -> M) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) f) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (max (succ u1) (succ u2)) (succ u3)} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4916 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (fun (_x : X -> M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : X -> M) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) _x) (AddHomClass.toFunLike.{max (max u1 u2) u3, max u1 u3, max (max u1 u2) u3} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4916 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddZeroClass.toAdd.{max u1 u3} (X -> M) (Pi.addZeroClass.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4916 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (AddZeroClass.toAdd.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (AddMonoidHomClass.toAddHomClass.{max (max u1 u2) u3, max u1 u3, max (max u1 u2) u3} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4916 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.addZeroClass.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4916 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddEquivClass.instAddMonoidHomClass.{max (max u1 u2) u3, max u1 u3, max (max u1 u2) u3} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4916 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.addZeroClass.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4916 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddEquiv.instAddEquivClassAddEquiv.{max u1 u3, max (max u1 u2) u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4916 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (Finsupp.lift.{u1, u2, u3} M R _inst_1 _inst_3 _inst_4 X) f) g) (Finsupp.sum.{u3, u2, u1} X R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) _inst_3 g (fun (x : X) (r : R) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4))))) r (f x)))
Case conversion may be inaccurate. Consider using '#align finsupp.lift_apply Finsupp.lift_applyₓ'. -/
@[simp]
theorem lift_apply (f) (g) : ((lift M R X) f) g = g.Sum fun x r => r • f x :=
@@ -898,7 +898,7 @@ theorem total_single (c : R) (a : α) : Finsupp.total α M R v (single a c) = c
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (x : Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u1 u2} (α -> M) 0 (OfNat.mk.{max u1 u2} (α -> M) 0 (Zero.zero.{max u1 u2} (α -> M) (Pi.instZero.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))))))) x) (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))))))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u3 u1} (α -> M) 0 (Zero.toOfNat0.{max u3 u1} (α -> M) (Pi.instZero.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.6475 : α) => M) (fun (i : α) => AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) _inst_3))))
+ forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u3 u1} (α -> M) 0 (Zero.toOfNat0.{max u3 u1} (α -> M) (Pi.instZero.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.6471 : α) => M) (fun (i : α) => AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) _inst_3))))
Case conversion may be inaccurate. Consider using '#align finsupp.total_zero_apply Finsupp.total_zero_applyₓ'. -/
theorem total_zero_apply (x : α →₀ R) : (Finsupp.total α M R 0) x = 0 := by
simp [Finsupp.total_apply]
@@ -910,7 +910,7 @@ variable (α M)
lean 3 declaration is
forall (α : Type.{u1}) (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], Eq.{max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u1 u2} (α -> M) 0 (OfNat.mk.{max u1 u2} (α -> M) 0 (Zero.zero.{max u1 u2} (α -> M) (Pi.instZero.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))))))) (OfNat.ofNat.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) 0 (OfNat.mk.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) 0 (Zero.zero.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.hasZero.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))
but is expected to have type
- forall (α : Type.{u3}) (M : Type.{u2}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Eq.{max (max (succ u3) (succ u2)) (succ u1)} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u3 u2} (α -> M) 0 (Zero.toOfNat0.{max u3 u2} (α -> M) (Pi.instZero.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.6475 : α) => M) (fun (i : α) => AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))))) (OfNat.ofNat.{max (max u3 u2) u1} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) 0 (Zero.toOfNat0.{max (max u3 u2) u1} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (LinearMap.instZeroLinearMap.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))
+ forall (α : Type.{u3}) (M : Type.{u2}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Eq.{max (max (succ u3) (succ u2)) (succ u1)} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u3 u2} (α -> M) 0 (Zero.toOfNat0.{max u3 u2} (α -> M) (Pi.instZero.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.6471 : α) => M) (fun (i : α) => AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))))) (OfNat.ofNat.{max (max u3 u2) u1} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) 0 (Zero.toOfNat0.{max (max u3 u2) u1} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (LinearMap.instZeroLinearMap.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))
Case conversion may be inaccurate. Consider using '#align finsupp.total_zero Finsupp.total_zeroₓ'. -/
@[simp]
theorem total_zero : Finsupp.total α M R 0 = 0 :=
@@ -1749,7 +1749,7 @@ variable {S}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] {S : Type.{u4}} [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (f : α -> R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) => (α -> R) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (coeFn.{max (succ (max u1 u2)) (succ (max (max u1 u3) u2)), max (succ (max u1 u2)) (succ (max (max u1 u3) u2))} (LinearMap.{u4, u4, max u1 u2, max (max u1 u3) u2} S S _inst_5 _inst_5 (RingHom.id.{u4} S 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(Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) (fun (_x : LinearMap.{u4, u4, max u1 u2, max (max u1 u3) u2} S S _inst_5 _inst_5 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) => (α -> M) -> (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4)) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, max (max u1 u3) u2} S S (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) f) (Finset.sum.{u2, u1} M α _inst_3 (Finset.univ.{u1} α _inst_1) (fun (i : α) => SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (f i) (v i)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (f : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> R) => M) f) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) v) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearMap.{u1, u1, max u3 u4, max u4 u3 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u3, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13965 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13965 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13965 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) f) (Finset.sum.{u4, u3} M α _inst_3 (Finset.univ.{u3} α _inst_1) (fun (i : α) => HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) (f i) (v i)))
+ forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M 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Case conversion may be inaccurate. Consider using '#align fintype.total_apply Fintype.total_applyₓ'. -/
theorem Fintype.total_apply (f) : Fintype.total R S v f = ∑ i, f i • v i :=
rfl
@@ -1759,7 +1759,7 @@ theorem Fintype.total_apply (f) : Fintype.total R S v f = ∑ i, f i • v i :=
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] {S : Type.{u4}} [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (i : α) (r : R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) => (α -> M) -> (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4)) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, max (max u1 u3) u2} S S (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) (Pi.single.{u1, u3} α (fun (ᾰ : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u1} α a b)) (fun (i : α) => MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) i r)) (SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) r (v i))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (i : α) (r : R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> R) => M) (Pi.single.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) v) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearMap.{u1, u1, max u3 u4, max u4 u3 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R 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(i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13965 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13965 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) (Pi.single.{u3, u2} α (fun (ᾰ : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) r (v i))
+ forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (i : α) (r : R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> R) => M) (Pi.single.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) v) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearMap.{u1, u1, max u3 u4, max u4 u3 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u3, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13959 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13959 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13959 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) (Pi.single.{u3, u2} α (fun (ᾰ : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) r (v i))
Case conversion may be inaccurate. Consider using '#align fintype.total_apply_single Fintype.total_apply_singleₓ'. -/
@[simp]
theorem Fintype.total_apply_single (i : α) (r : R) :
@@ -1775,7 +1775,7 @@ variable (S)
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] (S : Type.{u4}) [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (x : α -> R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))) M _inst_2 _inst_2 (Finsupp.addCommMonoid.{u1, 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(Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) x)
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (x : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) => M) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (α -> R) (fun (a : α -> R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> R) => Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) a) (SMulHomClass.toFunLike.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (α -> R) (AddMonoid.toZero.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (α -> R) (AddMonoid.toAddZeroClass.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (α -> R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u3 u2, max u3 u2, max u3 u2} R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) 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(a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (α -> R) (AddMonoid.toAddZeroClass.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (α -> R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u3 u2, max u3 u2, max u3 u2} R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u3 u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2)))))) (LinearEquiv.symm.{u2, u2, max u3 u2, max u3 u2} R R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (α -> R) _inst_2 _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (Finsupp.linearEquivFunOnFinite.{u2, u2, u3} R R α (Finite.of_fintype.{u3} α _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) _inst_2 (Semiring.toModule.{u2} R _inst_2))) x)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) v) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearMap.{u1, u1, max u3 u4, max u4 u3 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun 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(Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13965 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13965 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) x)
+ forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (x : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) => M) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (α -> R) (fun (a : α -> R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> R) => Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) a) (SMulHomClass.toFunLike.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (α -> R) (AddMonoid.toZero.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (α -> R) (AddMonoid.toAddZeroClass.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (α -> R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u3 u2, max u3 u2, max u3 u2} R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u3 u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2)))))) (LinearEquiv.symm.{u2, u2, max u3 u2, max u3 u2} R R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (α -> R) _inst_2 _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) _inst_2 (Semiring.toModule.{u2} R _inst_2))) x)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α 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_inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13959 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) x)
Case conversion may be inaccurate. Consider using '#align finsupp.total_eq_fintype_total_apply Finsupp.total_eq_fintype_total_applyₓ'. -/
theorem Finsupp.total_eq_fintype_total_apply (x : α → R) :
Finsupp.total α M R v ((Finsupp.linearEquivFunOnFinite R R α).symm x) = Fintype.total R S v x :=
@@ -1791,7 +1791,7 @@ theorem Finsupp.total_eq_fintype_total_apply (x : α → R) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] (S : Type.{u4}) [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (LinearMap.comp.{u3, u3, u3, max u1 u3, max u1 u3, u2} R R R (α -> R) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))) M _inst_2 _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHomCompTriple.right_ids.{u3, u3} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Finsupp.total.{u1, u2, u3} α M R _inst_2 _inst_3 _inst_4 v) (LinearEquiv.toLinearMap.{u3, u3, max u1 u3, max u1 u3} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHomInvPair.ids.{u3} R _inst_2) (RingHomInvPair.ids.{u3} R _inst_2) (α -> R) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))))) (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Pi.Function.module.{u1, 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(fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) => (α -> M) -> (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4)) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, max (max u1 u3) u2} S S (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)
but is expected to have type
- forall {α : Type.{u4}} {M : Type.{u3}} (R : Type.{u2}) [_inst_1 : Fintype.{u4} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u3} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u3} R S M (SMulZeroClass.toSMul.{u2, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u2, u3} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u3} S M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u1, u3} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (LinearMap.comp.{u2, u2, u2, max u4 u2, max u4 u2, u3} R R R (α -> R) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) M _inst_2 _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => 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(Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u4, max (max u2 u3) u4} S S (α -> M) (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u4, u3} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u4 u2, u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u4, u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13965 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u4 u2, u3} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u4, u3, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)
+ forall {α : Type.{u4}} {M : Type.{u3}} (R : Type.{u2}) [_inst_1 : Fintype.{u4} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u3} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u3} R S M (SMulZeroClass.toSMul.{u2, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u2, u3} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u3} S M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u1, u3} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (LinearMap.comp.{u2, u2, u2, max u4 u2, max u4 u2, u3} R R R (α -> R) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) M _inst_2 _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomCompTriple.ids.{u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Finsupp.total.{u4, u3, u2} α M R _inst_2 _inst_3 _inst_4 v) (LinearEquiv.toLinearMap.{u2, u2, max u4 u2, max u4 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u4, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (LinearEquiv.symm.{u2, u2, max u4 u2, max u4 u2} R R (Finsupp.{u4, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (α -> R) _inst_2 _inst_2 (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (Finsupp.linearEquivFunOnFinite.{u2, u2, u4} R R α (Finite.of_fintype.{u4} α _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) _inst_2 (Semiring.toModule.{u2} R _inst_2))))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), max (max (succ u2) (succ u3)) (succ u4)} (LinearMap.{u1, u1, max u4 u3, max u3 u4 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u4, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13959 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u4 u2, u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u4, u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13959 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u4 u2, u3} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u4, max (max u2 u3) u4} S S (α -> M) (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u4, u3} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u4 u2, u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u4, u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13959 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u4 u2, u3} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u4, u3, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)
Case conversion may be inaccurate. Consider using '#align finsupp.total_eq_fintype_total Finsupp.total_eq_fintype_totalₓ'. -/
theorem Finsupp.total_eq_fintype_total :
(Finsupp.total α M R v).comp (Finsupp.linearEquivFunOnFinite R R α).symm.toLinearMap =
@@ -1805,7 +1805,7 @@ variable {S}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] {S : Type.{u4}} [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{succ u2} (Submodule.{u3, u2} R M _inst_2 _inst_3 _inst_4) (LinearMap.range.{u3, u3, max u1 u3, u2, max (max u1 u3) u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (LinearMap.semilinearMapClass.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (RingHomSurjective.ids.{u3} R _inst_2) (coeFn.{max (succ (max u1 u2)) (succ (max (max u1 u3) u2)), max (succ (max u1 u2)) (succ (max (max u1 u3) u2))} (LinearMap.{u4, u4, max u1 u2, max (max u1 u3) u2} S S _inst_5 _inst_5 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) (fun (_x : LinearMap.{u4, u4, max u1 u2, max (max u1 u3) u2} S S _inst_5 _inst_5 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) => (α -> M) -> (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4)) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, max (max u1 u3) u2} S S (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)) (Submodule.span.{u3, u2} R M _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u1} M α v))
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u4}} (R : Type.{u3}) [_inst_1 : Fintype.{u2} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u3, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u1, u4} R S M (SMulZeroClass.toSMul.{u3, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u4} R M (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u4} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u3, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{succ u4} (Submodule.{u3, u4} R M _inst_2 _inst_3 _inst_4) (LinearMap.range.{u3, u3, max u2 u3, u4, max (max u2 u4) u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) v) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (RingHomSurjective.ids.{u3} R _inst_2) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearMap.{u1, u1, max u2 u4, max u4 u2 u3} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u2, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13965 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.module.{u2, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13965 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u2 u3, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u2, max (max u3 u4) u2} S S (α -> M) (LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u2, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.module.{u2, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13965 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u2 u3, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u2, u4, u3, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)) (Submodule.span.{u3, u4} R M _inst_2 _inst_3 _inst_4 (Set.range.{u4, succ u2} M α v))
+ forall {α : Type.{u2}} {M : Type.{u4}} (R : Type.{u3}) [_inst_1 : Fintype.{u2} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u3, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u1, u4} R S M (SMulZeroClass.toSMul.{u3, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u4} R M (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u4} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u3, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{succ u4} (Submodule.{u3, u4} R M _inst_2 _inst_3 _inst_4) (LinearMap.range.{u3, u3, max u2 u3, u4, max (max u2 u4) u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) v) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (RingHomSurjective.ids.{u3} R _inst_2) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearMap.{u1, u1, max u2 u4, max u4 u2 u3} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u2, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13959 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun 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NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u2, max (max u3 u4) u2} S S (α -> M) (LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u2, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.module.{u2, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13959 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u2 u3, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13971 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u2, u4, u3, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)) (Submodule.span.{u3, u4} R M _inst_2 _inst_3 _inst_4 (Set.range.{u4, succ u2} M α v))
Case conversion may be inaccurate. Consider using '#align fintype.range_total Fintype.range_totalₓ'. -/
@[simp]
theorem Fintype.range_total : (Fintype.total R S v).range = Submodule.span R (Set.range v) := by
@@ -2055,7 +2055,7 @@ theorem splittingOfFinsuppSurjective_injective (f : M →ₗ[R] α →₀ R) (s
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3)
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16534 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u1) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16534 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16534 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16534 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16548 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) _inst_3)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16528 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u1) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16528 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16528 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16528 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16542 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) _inst_3)
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective LinearMap.splittingOfFunOnFintypeSurjectiveₓ'. -/
-- See also `linear_map.splitting_of_finsupp_surjective`
/-- A surjective linear map to functions on a finite type has a splitting. -/
@@ -2069,7 +2069,7 @@ def splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R) (s
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Eq.{succ (max u3 u1)} (LinearMap.{u1, u1, max u3 u1, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (LinearMap.comp.{u1, u1, u1, max u3 u1, u2, max u3 u1} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomCompTriple.right_ids.{u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u1, max u3 u1} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16614 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16614 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16614 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16614 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Eq.{max (succ u2) (succ u3)} (LinearMap.{u2, u2, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16548 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16614 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.comp.{u2, u2, u2, max u2 u3, u1, max u2 u3} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16548 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16614 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u2, max u2 u3} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16548 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16608 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16608 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16608 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16608 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Eq.{max (succ u2) (succ u3)} (LinearMap.{u2, u2, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16542 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16608 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.comp.{u2, u2, u2, max u2 u3, u1, max u2 u3} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16542 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16608 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u2, max u2 u3} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16542 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)))
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective_splits LinearMap.splittingOfFunOnFintypeSurjective_splitsₓ'. -/
theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : f.comp (splittingOfFunOnFintypeSurjective f s) = LinearMap.id :=
@@ -2085,7 +2085,7 @@ theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R]
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Function.LeftInverse.{max (succ u3) (succ u1), succ u2} (α -> R) M (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f) (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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but is expected to have type
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16548 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16548 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => 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+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16738 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), 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Case conversion may be inaccurate. Consider using '#align linear_map.left_inverse_splitting_of_fun_on_fintype_surjective LinearMap.leftInverse_splittingOfFunOnFintypeSurjectiveₓ'. -/
theorem leftInverse_splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : LeftInverse f (splittingOfFunOnFintypeSurjective f s) := fun g =>
@@ -2096,7 +2096,7 @@ theorem leftInverse_splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Function.Injective.{max (succ u3) (succ u1), succ u2} (α -> R) M (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) (fun (_x : LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) => (α -> R) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, u2} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16800 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16800 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16800 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16800 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Function.Injective.{max (succ u2) (succ u3), succ u1} (α -> R) M (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16548 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16548 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16548 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16794 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16794 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16794 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16794 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Function.Injective.{max (succ u2) (succ u3), succ u1} (α -> R) M (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16542 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16542 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16542 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective_injective LinearMap.splittingOfFunOnFintypeSurjective_injectiveₓ'. -/
theorem splittingOfFunOnFintypeSurjective_injective [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : Injective (splittingOfFunOnFintypeSurjective f s) :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/62e8311c791f02c47451bf14aa2501048e7c2f33
@@ -80,7 +80,7 @@ variable [AddCommMonoid P] [Module R P]
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], α -> (LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))
but is expected to have type
- forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], α -> (LinearMap.{u3, u3, u2, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))
+ forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], α -> (LinearMap.{u3, u3, u2, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))
Case conversion may be inaccurate. Consider using '#align finsupp.lsingle Finsupp.lsingleₓ'. -/
/-- Interpret `finsupp.single a` as a linear map. -/
def lsingle (a : α) : M →ₗ[R] α →₀ M :=
@@ -91,7 +91,7 @@ def lsingle (a : α) : M →ₗ[R] α →₀ M :=
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} [_inst_1 : Semiring.{u4} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] {{φ : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6}} {{ψ : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6}}, (forall (a : α) (b : M), Eq.{succ u3} N (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (fun (_x : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) => (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) -> N) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) φ (Finsupp.single.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) a b)) (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (fun (_x : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) => (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) -> N) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) ψ (Finsupp.single.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) a b))) -> (Eq.{max (succ (max u1 u2)) (succ u3)} (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) φ ψ)
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u3}} {N : Type.{u1}} {R : Type.{u4}} [_inst_1 : Semiring.{u4} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u4, u3} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : Module.{u4, u1} R N _inst_1 _inst_5] {{φ : LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6}} {{ψ : LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6}}, (forall (a : α) (b : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => N) (Finsupp.single.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) a b)) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u3), succ u1} (LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (fun (_x : Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u2 u3, u1} R R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) φ (Finsupp.single.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) a b)) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u3), succ u1} (LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (fun (_x : Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u2 u3, u1} R R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) ψ (Finsupp.single.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) a b))) -> (Eq.{max (max (succ u2) (succ u3)) (succ u1)} (LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) φ ψ)
+ forall {α : Type.{u2}} {M : Type.{u3}} {N : Type.{u1}} {R : Type.{u4}} [_inst_1 : Semiring.{u4} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u4, u3} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : Module.{u4, u1} R N _inst_1 _inst_5] {{φ : LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6}} {{ψ : LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6}}, (forall (a : α) (b : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => N) (Finsupp.single.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) a b)) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u3), succ u1} (LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (fun (_x : Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u2 u3, u1} R R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) φ (Finsupp.single.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) a b)) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u3), succ u1} (LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (fun (_x : Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u2 u3, u1} R R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) ψ (Finsupp.single.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) a b))) -> (Eq.{max (max (succ u2) (succ u3)) (succ u1)} (LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) φ ψ)
Case conversion may be inaccurate. Consider using '#align finsupp.lhom_ext Finsupp.lhom_extₓ'. -/
/-- Two `R`-linear maps from `finsupp X M` which agree on each `single x y` agree everywhere. -/
theorem lhom_ext ⦃φ ψ : (α →₀ M) →ₗ[R] N⦄ (h : ∀ a b, φ (single a b) = ψ (single a b)) : φ = ψ :=
@@ -102,7 +102,7 @@ theorem lhom_ext ⦃φ ψ : (α →₀ M) →ₗ[R] N⦄ (h : ∀ a b, φ (singl
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} [_inst_1 : Semiring.{u4} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] {{φ : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6}} {{ψ : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6}}, (forall (a : α), Eq.{max (succ u2) (succ u3)} (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (LinearMap.comp.{u4, u4, u4, u2, max u1 u2, u3} R R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 _inst_4 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomCompTriple.right_ids.{u4, u4} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) φ (Finsupp.lsingle.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4 a)) (LinearMap.comp.{u4, u4, u4, u2, max u1 u2, u3} R R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 _inst_4 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomCompTriple.right_ids.{u4, u4} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) ψ (Finsupp.lsingle.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4 a))) -> (Eq.{max (succ (max u1 u2)) (succ u3)} (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) φ ψ)
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u3}} {N : Type.{u1}} {R : Type.{u4}} [_inst_1 : Semiring.{u4} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u4, u3} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : Module.{u4, u1} R N _inst_1 _inst_5] {{φ : LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6}} {{ψ : LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6}}, (forall (a : α), Eq.{max (succ u3) (succ u1)} (LinearMap.{u4, u4, u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (LinearMap.comp.{u4, u4, u4, u3, max u2 u3, u1} R R R M (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N _inst_1 _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 _inst_4 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomCompTriple.ids.{u4, u4} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) φ (Finsupp.lsingle.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4 a)) (LinearMap.comp.{u4, u4, u4, u3, max u2 u3, u1} R R R M (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N _inst_1 _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 _inst_4 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomCompTriple.ids.{u4, u4} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) ψ (Finsupp.lsingle.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4 a))) -> (Eq.{max (max (succ u2) (succ u3)) (succ u1)} (LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) φ ψ)
+ forall {α : Type.{u2}} {M : Type.{u3}} {N : Type.{u1}} {R : Type.{u4}} [_inst_1 : Semiring.{u4} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u4, u3} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : Module.{u4, u1} R N _inst_1 _inst_5] {{φ : LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6}} {{ψ : LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6}}, (forall (a : α), Eq.{max (succ u3) (succ u1)} (LinearMap.{u4, u4, u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (LinearMap.comp.{u4, u4, u4, u3, max u2 u3, u1} R R R M (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N _inst_1 _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 _inst_4 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomCompTriple.ids.{u4, u4} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) φ (Finsupp.lsingle.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4 a)) (LinearMap.comp.{u4, u4, u4, u3, max u2 u3, u1} R R R M (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N _inst_1 _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 _inst_4 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomCompTriple.ids.{u4, u4} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) ψ (Finsupp.lsingle.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4 a))) -> (Eq.{max (max (succ u2) (succ u3)) (succ u1)} (LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_5 (Finsupp.module.{u2, u3, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) φ ψ)
Case conversion may be inaccurate. Consider using '#align finsupp.lhom_ext' Finsupp.lhom_ext'ₓ'. -/
/-- Two `R`-linear maps from `finsupp X M` which agree on each `single x y` agree everywhere.
@@ -119,7 +119,7 @@ theorem lhom_ext' ⦃φ ψ : (α →₀ M) →ₗ[R] N⦄ (h : ∀ a, φ.comp (l
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], α -> (LinearMap.{u3, u3, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4)
but is expected to have type
- forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], α -> (LinearMap.{u3, u3, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4)
+ forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], α -> (LinearMap.{u3, u3, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4)
Case conversion may be inaccurate. Consider using '#align finsupp.lapply Finsupp.lapplyₓ'. -/
/-- Interpret `λ (f : α →₀ M), f a` as a linear map. -/
def lapply (a : α) : (α →₀ M) →ₗ[R] M :=
@@ -130,7 +130,7 @@ def lapply (a : α) : (α →₀ M) →ₗ[R] M :=
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], LinearMap.{u3, u3, max u1 u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (α -> M) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Pi.Function.module.{u1, u3, u2} α R M _inst_1 _inst_3 _inst_4)
but is expected to have type
- forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], LinearMap.{u3, u3, max u2 u1, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (α -> M) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Pi.module.{u1, u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.497 : α) => M) R _inst_1 (fun (i : α) => _inst_3) (fun (i : α) => _inst_4))
+ forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], LinearMap.{u3, u3, max u2 u1, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (α -> M) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Pi.module.{u1, u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.497 : α) => M) R _inst_1 (fun (i : α) => _inst_3) (fun (i : α) => _inst_4))
Case conversion may be inaccurate. Consider using '#align finsupp.lcoe_fun Finsupp.lcoeFunₓ'. -/
/-- Forget that a function is finitely supported.
@@ -154,7 +154,7 @@ variable (s : Set α)
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α), LinearMap.{u3, u3, max u1 u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) M R _inst_1 _inst_3 _inst_4)
but is expected to have type
- forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α), LinearMap.{u3, u3, max u2 u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u1, u2} (Set.Elem.{u1} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u1, u2} (Set.Elem.{u1} α s) M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u3} (Set.Elem.{u1} α s) M R _inst_1 _inst_3 _inst_4)
+ forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α), LinearMap.{u3, u3, max u2 u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u1, u2} (Set.Elem.{u1} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u1, u2} (Set.Elem.{u1} α s) M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u2, u3} (Set.Elem.{u1} α s) M R _inst_1 _inst_3 _inst_4)
Case conversion may be inaccurate. Consider using '#align finsupp.lsubtype_domain Finsupp.lsubtypeDomainₓ'. -/
/-- Interpret `finsupp.subtype_domain s` as a linear map. -/
def lsubtypeDomain : (α →₀ M) →ₗ[R] s →₀ M
@@ -168,7 +168,7 @@ def lsubtypeDomain : (α →₀ M) →ₗ[R] s →₀ M
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α) (f : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))), Eq.{max (succ u1) (succ u2)} (Finsupp.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u3, u3, max u1 u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) M R _inst_1 _inst_3 _inst_4)) (fun (_x : LinearMap.{u3, u3, max u1 u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) M R _inst_1 _inst_3 _inst_4)) => (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) -> (Finsupp.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))))) (LinearMap.hasCoeToFun.{u3, u3, max u1 u2, max u1 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lsubtypeDomain.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s) f) (Finsupp.subtypeDomain.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) f)
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (f : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Finsupp.{u3, u2} (Set.Elem.{u3} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) f) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearMap.{u1, u1, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} (Set.Elem.{u3} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} (Set.Elem.{u3} α s) M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} (Set.Elem.{u3} α s) M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (_x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Finsupp.{u3, u2} (Set.Elem.{u3} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u2, max u3 u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} (Set.Elem.{u3} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} (Set.Elem.{u3} α s) M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} (Set.Elem.{u3} α s) M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lsubtypeDomain.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) f) (Finsupp.subtypeDomain.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (fun (x : α) => Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) x s) f)
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (f : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Finsupp.{u3, u2} (Set.Elem.{u3} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) f) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearMap.{u1, u1, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} (Set.Elem.{u3} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} (Set.Elem.{u3} α s) M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} (Set.Elem.{u3} α s) M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (_x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Finsupp.{u3, u2} (Set.Elem.{u3} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u2, max u3 u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} (Set.Elem.{u3} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} (Set.Elem.{u3} α s) M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} (Set.Elem.{u3} α s) M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lsubtypeDomain.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) f) (Finsupp.subtypeDomain.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (fun (x : α) => Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) x s) f)
Case conversion may be inaccurate. Consider using '#align finsupp.lsubtype_domain_apply Finsupp.lsubtypeDomain_applyₓ'. -/
theorem lsubtypeDomain_apply (f : α →₀ M) :
(lsubtypeDomain s : (α →₀ M) →ₗ[R] s →₀ M) f = subtypeDomain (fun x => x ∈ s) f :=
@@ -181,7 +181,7 @@ end LsubtypeDomain
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (a : α) (b : M), Eq.{max (succ u1) (succ u2)} (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (fun (_x : LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) => M -> (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))))) (LinearMap.hasCoeToFun.{u3, u3, u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lsingle.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a) b) (Finsupp.single.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) a b)
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (a : α) (b : M), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) b) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a) b) (Finsupp.single.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) a b)
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (a : α) (b : M), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) b) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a) b) (Finsupp.single.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) a b)
Case conversion may be inaccurate. Consider using '#align finsupp.lsingle_apply Finsupp.lsingle_applyₓ'. -/
@[simp]
theorem lsingle_apply (a : α) (b : M) : (lsingle a : M →ₗ[R] α →₀ M) b = single a b :=
@@ -190,9 +190,9 @@ theorem lsingle_apply (a : α) (b : M) : (lsingle a : M →ₗ[R] α →₀ M) b
/- warning: finsupp.lapply_apply -> Finsupp.lapply_apply is a dubious translation:
lean 3 declaration is
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+ forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (a : α) (f : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))), Eq.{succ u2} M (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (LinearMap.{u3, u3, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4) => (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u2, u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lapply.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a) f) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (fun (_x : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) => α -> M) (Finsupp.coeFun.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) f a)
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (a : α) (f : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => M) f) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), succ u2} (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (_x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u2, u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lapply.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a) f) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) α (fun (_x : α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) _x) (Finsupp.funLike.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) f a)
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (a : α) (f : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => M) f) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), succ u2} (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (_x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u2, u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lapply.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a) f) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) α (fun (_x : α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) _x) (Finsupp.funLike.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) f a)
Case conversion may be inaccurate. Consider using '#align finsupp.lapply_apply Finsupp.lapply_applyₓ'. -/
@[simp]
theorem lapply_apply (a : α) (f : α →₀ M) : (lapply a : (α →₀ M) →ₗ[R] M) f = f a :=
@@ -203,7 +203,7 @@ theorem lapply_apply (a : α) (f : α →₀ M) : (lapply a : (α →₀ M) →
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (a : α), Eq.{succ u2} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) (LinearMap.ker.{u3, u3, u2, max u1 u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u3, u3, u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lsingle.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a)) (Bot.bot.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasBot.{u3, u2} R M _inst_1 _inst_3 _inst_4))
but is expected to have type
- forall {α : Type.{u1}} {M : Type.{u3}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_1 _inst_3] (a : α), Eq.{succ u3} (Submodule.{u2, u3} R M _inst_1 _inst_3 _inst_4) (LinearMap.ker.{u2, u2, u3, max u1 u3, max u1 u3} R R M (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u3} α M _inst_3) _inst_4 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u2} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u1, u3} α M _inst_3) _inst_4 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u2} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u3, max u1 u3} R R M (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u3} α M _inst_3) _inst_4 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u2} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.lsingle.{u1, u3, u2} α M R _inst_1 _inst_3 _inst_4 a)) (Bot.bot.{u3} (Submodule.{u2, u3} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u2, u3} R M _inst_1 _inst_3 _inst_4))
+ forall {α : Type.{u1}} {M : Type.{u3}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_1 _inst_3] (a : α), Eq.{succ u3} (Submodule.{u2, u3} R M _inst_1 _inst_3 _inst_4) (LinearMap.ker.{u2, u2, u3, max u1 u3, max u1 u3} R R M (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u3} α M _inst_3) _inst_4 (Finsupp.module.{u1, u3, u2} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u1, u3} α M _inst_3) _inst_4 (Finsupp.module.{u1, u3, u2} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u3, max u1 u3} R R M (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u3} α M _inst_3) _inst_4 (Finsupp.module.{u1, u3, u2} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.lsingle.{u1, u3, u2} α M R _inst_1 _inst_3 _inst_4 a)) (Bot.bot.{u3} (Submodule.{u2, u3} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u2, u3} R M _inst_1 _inst_3 _inst_4))
Case conversion may be inaccurate. Consider using '#align finsupp.ker_lsingle Finsupp.ker_lsingleₓ'. -/
@[simp]
theorem ker_lsingle (a : α) : (lsingle a : M →ₗ[R] α →₀ M).ker = ⊥ :=
@@ -214,7 +214,7 @@ theorem ker_lsingle (a : α) : (lsingle a : M →ₗ[R] α →₀ M).ker = ⊥ :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α) (t : Set.{u1} α), (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) s t) -> (LE.le.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toLE.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))))) (supᵢ.{max u1 u2, succ u1} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => supᵢ.{max u1 u2, 0} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LinearMap.range.{u3, u3, u2, max u1 u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u3, u3, u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R _inst_1) (Finsupp.lsingle.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a)))) (infᵢ.{max u1 u2, succ u1} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasInf.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) α (fun (a : α) => infᵢ.{max u1 u2, 0} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasInf.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a t) => LinearMap.ker.{u3, u3, max u1 u2, u2, max u1 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4) (LinearMap.semilinearMapClass.{u3, u3, max u1 u2, u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lapply.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a)))))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (t : Set.{u3} α), (Disjoint.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} α) (Preorder.toLE.{u3} (Set.{u3} α) (PartialOrder.toPreorder.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) s t) -> (LE.le.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toLE.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))))) (supᵢ.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => supᵢ.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) (fun (H : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a)))) (infᵢ.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) α (fun (a : α) => infᵢ.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a t) (fun (H : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a t) => LinearMap.ker.{u1, u1, max u3 u2, u2, max u3 u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u3 u2, u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lapply.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a)))))
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (t : Set.{u3} α), (Disjoint.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} α) (Preorder.toLE.{u3} (Set.{u3} α) (PartialOrder.toPreorder.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) s t) -> (LE.le.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toLE.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))))) (supᵢ.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => supᵢ.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) (fun (H : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a)))) (infᵢ.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) α (fun (a : α) => infᵢ.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a t) (fun (H : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a t) => LinearMap.ker.{u1, u1, max u3 u2, u2, max u3 u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u3 u2, u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lapply.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a)))))
Case conversion may be inaccurate. Consider using '#align finsupp.lsingle_range_le_ker_lapply Finsupp.lsingle_range_le_ker_lapplyₓ'. -/
theorem lsingle_range_le_ker_lapply (s t : Set α) (h : Disjoint s t) :
(⨆ a ∈ s, (lsingle a : M →ₗ[R] α →₀ M).range) ≤ ⨅ a ∈ t, ker (lapply a : (α →₀ M) →ₗ[R] M) :=
@@ -230,7 +230,7 @@ theorem lsingle_range_le_ker_lapply (s t : Set α) (h : Disjoint s t) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], LE.le.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toLE.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))))) (infᵢ.{max u1 u2, succ u1} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasInf.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) α (fun (a : α) => LinearMap.ker.{u3, u3, max u1 u2, u2, max u1 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4) (LinearMap.semilinearMapClass.{u3, u3, max u1 u2, u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_3 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lapply.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a))) (Bot.bot.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasBot.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], LE.le.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toLE.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))))) (infᵢ.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) α (fun (a : α) => LinearMap.ker.{u1, u1, max u3 u2, u2, max u3 u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u3 u2, u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lapply.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a))) (Bot.bot.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instBotSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], LE.le.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toLE.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))))) (infᵢ.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) α (fun (a : α) => LinearMap.ker.{u1, u1, max u3 u2, u2, max u3 u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u3 u2, u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_3 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lapply.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a))) (Bot.bot.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instBotSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))
Case conversion may be inaccurate. Consider using '#align finsupp.infi_ker_lapply_le_bot Finsupp.infᵢ_ker_lapply_le_botₓ'. -/
theorem infᵢ_ker_lapply_le_bot : (⨅ a, ker (lapply a : (α →₀ M) →ₗ[R] M)) ≤ ⊥ :=
by
@@ -242,7 +242,7 @@ theorem infᵢ_ker_lapply_le_bot : (⨅ a, ker (lapply a : (α →₀ M) →ₗ[
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], Eq.{succ (max u1 u2)} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (supᵢ.{max u1 u2, succ u1} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => LinearMap.range.{u3, u3, u2, max u1 u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u3, u3, u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R _inst_1) (Finsupp.lsingle.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a))) (Top.top.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasTop.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (supᵢ.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a))) (Top.top.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instTopSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (supᵢ.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a))) (Top.top.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instTopSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))
Case conversion may be inaccurate. Consider using '#align finsupp.supr_lsingle_range Finsupp.supᵢ_lsingle_rangeₓ'. -/
theorem supᵢ_lsingle_range : (⨆ a, (lsingle a : M →ₗ[R] α →₀ M).range) = ⊤ :=
by
@@ -255,7 +255,7 @@ theorem supᵢ_lsingle_range : (⨆ a, (lsingle a : M →ₗ[R] α →₀ M).ran
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α) (t : Set.{u1} α), (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) s t) -> (Disjoint.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) (Submodule.orderBot.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (supᵢ.{max u1 u2, succ u1} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => supᵢ.{max u1 u2, 0} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LinearMap.range.{u3, u3, u2, max u1 u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u3, u3, u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R _inst_1) (Finsupp.lsingle.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a)))) (supᵢ.{max u1 u2, succ u1} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => supᵢ.{max u1 u2, 0} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a t) => LinearMap.range.{u3, u3, u2, max u1 u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u3, u3, u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R _inst_1) (Finsupp.lsingle.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a)))))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (t : Set.{u3} α), (Disjoint.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} α) (Preorder.toLE.{u3} (Set.{u3} α) (PartialOrder.toPreorder.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) s t) -> (Disjoint.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (supᵢ.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => supᵢ.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) (fun (H : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a)))) (supᵢ.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => supᵢ.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a t) (fun (H : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a t) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a)))))
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (t : Set.{u3} α), (Disjoint.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} α) (Preorder.toLE.{u3} (Set.{u3} α) (PartialOrder.toPreorder.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) s t) -> (Disjoint.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (supᵢ.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => supᵢ.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) (fun (H : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a)))) (supᵢ.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) α (fun (a : α) => supᵢ.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a t) (fun (H : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a t) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R M (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) _inst_4 (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.lsingle.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 a)))))
Case conversion may be inaccurate. Consider using '#align finsupp.disjoint_lsingle_lsingle Finsupp.disjoint_lsingle_lsingleₓ'. -/
theorem disjoint_lsingle_lsingle (s t : Set α) (hs : Disjoint s t) :
Disjoint (⨆ a ∈ s, (lsingle a : M →ₗ[R] α →₀ M).range)
@@ -279,7 +279,7 @@ theorem disjoint_lsingle_lsingle (s t : Set α) (hs : Disjoint s t) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u2} M) (a : α), Eq.{succ (max u1 u2)} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.span.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Set.image.{u2, max u1 u2} M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.single.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) a) s)) (Submodule.map.{u3, u3, u2, max u1 u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomSurjective.ids.{u3} R _inst_1) (LinearMap.{u3, u3, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u3, u3, u2, max u1 u2} R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_4 (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lsingle.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 a) (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 s))
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u3}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u1, u3} R M _inst_1 _inst_3] (s : Set.{u3} M) (a : α), Eq.{max (succ u2) (succ u3)} (Submodule.{u1, max u3 u2} R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.span.{u1, max u3 u2} R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4) (Set.image.{u3, max u3 u2} M (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.single.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) a) s)) (Submodule.map.{u1, u1, u3, max u2 u3, max u2 u3} R R M (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_4 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.{u1, u1, u3, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_4 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u3, max u2 u3} R R M (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_4 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lsingle.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4 a) (Submodule.span.{u1, u3} R M _inst_1 _inst_3 _inst_4 s))
+ forall {α : Type.{u2}} {M : Type.{u3}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u1, u3} R M _inst_1 _inst_3] (s : Set.{u3} M) (a : α), Eq.{max (succ u2) (succ u3)} (Submodule.{u1, max u3 u2} R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) (Finsupp.module.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.span.{u1, max u3 u2} R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) (Finsupp.module.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4) (Set.image.{u3, max u3 u2} M (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.single.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) a) s)) (Submodule.map.{u1, u1, u3, max u2 u3, max u2 u3} R R M (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_4 (Finsupp.module.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.{u1, u1, u3, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_3 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_4 (Finsupp.module.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u3, max u2 u3} R R M (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) _inst_4 (Finsupp.module.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lsingle.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4 a) (Submodule.span.{u1, u3} R M _inst_1 _inst_3 _inst_4 s))
Case conversion may be inaccurate. Consider using '#align finsupp.span_single_image Finsupp.span_single_imageₓ'. -/
theorem span_single_image (s : Set M) (a : α) :
Submodule.span R (single a '' s) = (Submodule.span R s).map (lsingle a : M →ₗ[R] α →₀ M) := by
@@ -292,7 +292,7 @@ variable (M R)
lean 3 declaration is
forall {α : Type.{u1}} (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], (Set.{u1} α) -> (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))
but is expected to have type
- forall {α : Type.{u1}} (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], (Set.{u1} α) -> (Submodule.{u3, max u2 u1} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))
+ forall {α : Type.{u1}} (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], (Set.{u1} α) -> (Submodule.{u3, max u2 u1} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))
Case conversion may be inaccurate. Consider using '#align finsupp.supported Finsupp.supportedₓ'. -/
/-- `finsupp.supported M R s` is the `R`-submodule of all `p : α →₀ M` such that `p.support ⊆ s`. -/
def supported (s : Set α) : Submodule R (α →₀ M) :=
@@ -314,7 +314,7 @@ variable {M}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {s : Set.{u1} α} (p : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))), Iff (Membership.Mem.{max u1 u2, max u1 u2} (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) p (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} α) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (Finset.Set.hasCoeT.{u1} α))) (Finsupp.support.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) p)) s)
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {s : Set.{u3} α} (p : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))), Iff (Membership.mem.{max u3 u2, max u2 u3} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) p (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (HasSubset.Subset.{u3} (Set.{u3} α) (Set.instHasSubsetSet.{u3} α) (Finset.toSet.{u3} α (Finsupp.support.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) p)) s)
+ forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {s : Set.{u3} α} (p : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))), Iff (Membership.mem.{max u3 u2, max u2 u3} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) p (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (HasSubset.Subset.{u3} (Set.{u3} α) (Set.instHasSubsetSet.{u3} α) (Finset.toSet.{u3} α (Finsupp.support.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) p)) s)
Case conversion may be inaccurate. Consider using '#align finsupp.mem_supported Finsupp.mem_supportedₓ'. -/
theorem mem_supported {s : Set α} (p : α →₀ M) : p ∈ supported M R s ↔ ↑p.support ⊆ s :=
Iff.rfl
@@ -322,9 +322,9 @@ theorem mem_supported {s : Set α} (p : α →₀ M) : p ∈ supported M R s ↔
/- warning: finsupp.mem_supported' -> Finsupp.mem_supported' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {s : Set.{u1} α} (p : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))), Iff (Membership.Mem.{max u1 u2, max u1 u2} (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) p (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (forall (x : α), (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s)) -> (Eq.{succ u2} M (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (fun (_x : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) => α -> M) (Finsupp.hasCoeToFun.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) p x) (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))))))))
+ forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {s : Set.{u1} α} (p : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))), Iff (Membership.Mem.{max u1 u2, max u1 u2} (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) p (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (forall (x : α), (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s)) -> (Eq.{succ u2} M (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (fun (_x : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) => α -> M) (Finsupp.coeFun.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) p x) (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))))))))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {s : Set.{u3} α} (p : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))), Iff (Membership.mem.{max u3 u2, max u2 u3} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) p (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (forall (x : α), (Not (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) x s)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) x) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) α (fun (_x : α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) _x) (Finsupp.funLike.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) p x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) x) (AddMonoid.toZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) x) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) x) _inst_3))))))
+ forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {s : Set.{u3} α} (p : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))), Iff (Membership.mem.{max u3 u2, max u2 u3} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) p (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (forall (x : α), (Not (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) x s)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) x) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) α (fun (_x : α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) _x) (Finsupp.funLike.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) p x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) x) (AddMonoid.toZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) x) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) x) _inst_3))))))
Case conversion may be inaccurate. Consider using '#align finsupp.mem_supported' Finsupp.mem_supported'ₓ'. -/
/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ∉ » s) -/
theorem mem_supported' {s : Set α} (p : α →₀ M) :
@@ -337,7 +337,7 @@ theorem mem_supported' {s : Set α} (p : α →₀ M) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (p : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))), Membership.Mem.{max u1 u2, max u1 u2} (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) p (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} α) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (Finset.Set.hasCoeT.{u1} α))) (Finsupp.support.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) p)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (p : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))), Membership.mem.{max u3 u2, max u2 u3} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) p (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (Finset.toSet.{u3} α (Finsupp.support.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) p)))
+ forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (p : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))), Membership.mem.{max u3 u2, max u2 u3} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) p (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (Finset.toSet.{u3} α (Finsupp.support.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) p)))
Case conversion may be inaccurate. Consider using '#align finsupp.mem_supported_support Finsupp.mem_supported_supportₓ'. -/
theorem mem_supported_support (p : α →₀ M) : p ∈ Finsupp.supported M R (p.support : Set α) := by
rw [Finsupp.mem_supported]
@@ -347,7 +347,7 @@ theorem mem_supported_support (p : α →₀ M) : p ∈ Finsupp.supported M R (p
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {s : Set.{u1} α} {a : α} (b : M), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (Membership.Mem.{max u1 u2, max u1 u2} (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) (Finsupp.single.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) a b) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {s : Set.{u3} α} {a : α} (b : M), (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) -> (Membership.mem.{max u2 u3, max u2 u3} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) (Finsupp.single.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) a b) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s))
+ forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {s : Set.{u3} α} {a : α} (b : M), (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a s) -> (Membership.mem.{max u2 u3, max u2 u3} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) (Finsupp.single.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) a b) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s))
Case conversion may be inaccurate. Consider using '#align finsupp.single_mem_supported Finsupp.single_mem_supportedₓ'. -/
theorem single_mem_supported {s : Set α} {a : α} (b : M) (h : a ∈ s) :
single a b ∈ supported M R s :=
@@ -358,7 +358,7 @@ theorem single_mem_supported {s : Set α} {a : α} (b : M) (h : a ∈ s) :
lean 3 declaration is
forall {α : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] (s : Set.{u1} α), Eq.{succ (max u1 u2)} (Submodule.{u2, max u1 u2} R (Finsupp.{u1, u2} α R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Finsupp.supported.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1) s) (Submodule.span.{u2, max u1 u2} R (Finsupp.{u1, u2} α R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Set.image.{u1, max u1 u2} α (Finsupp.{u1, u2} α R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (fun (i : α) => Finsupp.single.{u1, u2} α R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) i (OfNat.ofNat.{u2} R 1 (OfNat.mk.{u2} R 1 (One.one.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))))) s))
but is expected to have type
- forall {α : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] (s : Set.{u2} α), Eq.{max (succ u2) (succ u1)} (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (Finsupp.supported.{u2, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s) (Submodule.span.{u1, max u1 u2} R (Finsupp.{u2, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Set.image.{u2, max u1 u2} α (Finsupp.{u2, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (fun (i : α) => Finsupp.single.{u2, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) i (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) s))
+ forall {α : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] (s : Set.{u2} α), Eq.{max (succ u2) (succ u1)} (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (Finsupp.supported.{u2, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s) (Submodule.span.{u1, max u1 u2} R (Finsupp.{u2, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Set.image.{u2, max u1 u2} α (Finsupp.{u2, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (fun (i : α) => Finsupp.single.{u2, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) i (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) s))
Case conversion may be inaccurate. Consider using '#align finsupp.supported_eq_span_single Finsupp.supported_eq_span_singleₓ'. -/
theorem supported_eq_span_single (s : Set α) :
supported R R s = span R ((fun i => single i 1) '' s) :=
@@ -380,7 +380,7 @@ variable (M R)
lean 3 declaration is
forall {α : Type.{u1}} (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α), LinearMap.{u3, u3, max u1 u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Submodule.addCommMonoid.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Submodule.module.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s))
but is expected to have type
- forall {α : Type.{u1}} (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α), LinearMap.{u3, u3, max u2 u1, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Subtype.{succ (max u1 u2)} (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u1 u2, max u1 u2} (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u3, max u2 u1} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u3, max u2 u1} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) x (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s))
+ forall {α : Type.{u1}} (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α), LinearMap.{u3, u3, max u2 u1, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Subtype.{succ (max u1 u2)} (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u1 u2, max u1 u2} (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u3, max u2 u1} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u3, max u2 u1} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) x (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s))
Case conversion may be inaccurate. Consider using '#align finsupp.restrict_dom Finsupp.restrictDomₓ'. -/
/-- Interpret `finsupp.filter s` as a linear map from `α →₀ M` to `supported M R s`. -/
def restrictDom (s : Set α) : (α →₀ M) →ₗ[R] supported M R s :=
@@ -399,7 +399,7 @@ section
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α) (l : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))), Eq.{max (succ u1) (succ u2)} (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) ((fun (a : Type.{max u1 u2}) (b : Sort.{max (succ u1) (succ u2)}) [self : HasLiftT.{succ (max u1 u2), max (succ u1) (succ u2)} a b] => self.0) (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, 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(SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (coeSubtype.{max (succ u1) (succ u2)} (Finsupp.{u1, u2} α M 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(RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.restrictDom.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) l)) (Finsupp.filter.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (fun (_x : α) => Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) _x s) l)
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (l : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))), Eq.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Subtype.val.{succ (max u3 u2)} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u3 u2, max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Set.{max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Set.instMembershipSet.{max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) x (SetLike.coe.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s))) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearMap.{u1, u1, max u2 u3, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) 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(AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s))) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (_x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Subtype.{succ (max u3 u2)} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u3 u2, max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) x (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u2, max u3 u2} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Subtype.{succ (max u3 u2)} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u3 u2, max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) x (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.restrictDom.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) l)) (Finsupp.filter.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (fun (_x : α) => Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) _x s) l)
Case conversion may be inaccurate. Consider using '#align finsupp.restrict_dom_apply Finsupp.restrictDom_applyₓ'. -/
@[simp]
theorem restrictDom_apply (s : Set α) (l : α →₀ M) :
@@ -413,7 +413,7 @@ end
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α), Eq.{succ (max u1 u2)} (LinearMap.{u3, u3, max u1 u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M 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but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α), Eq.{max (succ u3) (succ u2)} (LinearMap.{u1, u1, max u3 u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Subtype.{succ (max u3 u2)} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u3 u2, max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max 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+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α), Eq.{max (succ u3) (succ u2)} (LinearMap.{u1, u1, max u3 u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Subtype.{succ (max u3 u2)} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u3 u2, max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u3 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Case conversion may be inaccurate. Consider using '#align finsupp.restrict_dom_comp_subtype Finsupp.restrictDom_comp_subtypeₓ'. -/
theorem restrictDom_comp_subtype (s : Set α) :
(restrictDom M R s).comp (Submodule.subtype _) = LinearMap.id :=
@@ -427,7 +427,7 @@ theorem restrictDom_comp_subtype (s : Set α) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α), Eq.{succ (max u1 u2)} (Submodule.{u3, max u1 u2} R (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M 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but is expected to have type
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+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α), Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u3 u2} R (Subtype.{succ (max u3 u2)} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u3 u2, max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) 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R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) x (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s))) (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) 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(Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) x (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.restrictDom.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (Top.top.{max u3 u2} (Submodule.{u1, max u3 u2} R (Subtype.{succ (max u3 u2)} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u3 u2, max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) x (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s))) _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s))) (Submodule.instTopSubmodule.{u1, max u3 u2} R (Subtype.{succ (max u3 u2)} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u3 u2, max u3 u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) x (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s))) _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s))))
Case conversion may be inaccurate. Consider using '#align finsupp.range_restrict_dom Finsupp.range_restrictDomₓ'. -/
theorem range_restrictDom (s : Set α) : (restrictDom M R s).range = ⊤ :=
range_eq_top.2 <|
@@ -438,7 +438,7 @@ theorem range_restrictDom (s : Set α) : (restrictDom M R s).range = ⊤ :=
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s t) -> (LE.le.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toLE.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))))) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 t))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {s : Set.{u3} α} {t : Set.{u3} α}, (HasSubset.Subset.{u3} (Set.{u3} α) (Set.instHasSubsetSet.{u3} α) s t) -> (LE.le.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toLE.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))))) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 t))
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {s : Set.{u3} α} {t : Set.{u3} α}, (HasSubset.Subset.{u3} (Set.{u3} α) (Set.instHasSubsetSet.{u3} α) s t) -> (LE.le.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toLE.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))))) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 t))
Case conversion may be inaccurate. Consider using '#align finsupp.supported_mono Finsupp.supported_monoₓ'. -/
theorem supported_mono {s t : Set α} (st : s ⊆ t) : supported M R s ≤ supported M R t := fun l h =>
Set.Subset.trans h st
@@ -448,7 +448,7 @@ theorem supported_mono {s t : Set α} (st : s ⊆ t) : supported M R s ≤ suppo
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], Eq.{succ (max u1 u2)} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α))) (Bot.bot.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasBot.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (EmptyCollection.emptyCollection.{u3} (Set.{u3} α) (Set.instEmptyCollectionSet.{u3} α))) (Bot.bot.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instBotSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (EmptyCollection.emptyCollection.{u3} (Set.{u3} α) (Set.instEmptyCollectionSet.{u3} α))) (Bot.bot.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instBotSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))
Case conversion may be inaccurate. Consider using '#align finsupp.supported_empty Finsupp.supported_emptyₓ'. -/
@[simp]
theorem supported_empty : supported M R (∅ : Set α) = ⊥ :=
@@ -459,7 +459,7 @@ theorem supported_empty : supported M R (∅ : Set α) = ⊥ :=
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], Eq.{succ (max u1 u2)} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (Set.univ.{u1} α)) (Top.top.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasTop.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (Set.univ.{u3} α)) (Top.top.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instTopSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (Set.univ.{u3} α)) (Top.top.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instTopSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))
Case conversion may be inaccurate. Consider using '#align finsupp.supported_univ Finsupp.supported_univₓ'. -/
@[simp]
theorem supported_univ : supported M R (Set.univ : Set α) = ⊤ :=
@@ -470,7 +470,7 @@ theorem supported_univ : supported M R (Set.univ : Set α) = ⊤ :=
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {δ : Type.{u4}} (s : δ -> (Set.{u1} α)), Eq.{succ (max u1 u2)} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (Set.unionᵢ.{u1, succ u4} α δ (fun (i : δ) => s i))) (supᵢ.{max u1 u2, succ u4} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))) δ (fun (i : δ) => Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (s i)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {δ : Type.{u4}} (s : δ -> (Set.{u3} α)), Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (Set.unionᵢ.{u3, succ u4} α δ (fun (i : δ) => s i))) (supᵢ.{max u2 u3, succ u4} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) δ (fun (i : δ) => Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (s i)))
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {δ : Type.{u4}} (s : δ -> (Set.{u3} α)), Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (Set.unionᵢ.{u3, succ u4} α δ (fun (i : δ) => s i))) (supᵢ.{max u2 u3, succ u4} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) δ (fun (i : δ) => Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (s i)))
Case conversion may be inaccurate. Consider using '#align finsupp.supported_Union Finsupp.supported_unionᵢₓ'. -/
theorem supported_unionᵢ {δ : Type _} (s : δ → Set α) :
supported M R (⋃ i, s i) = ⨆ i, supported M R (s i) :=
@@ -494,7 +494,7 @@ theorem supported_unionᵢ {δ : Type _} (s : δ → Set α) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α) (t : Set.{u1} α), Eq.{succ (max u1 u2)} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) (Sup.sup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SemilatticeSup.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Lattice.toSemilatticeSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))))) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 t))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (t : Set.{u3} α), Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (Union.union.{u3} (Set.{u3} α) (Set.instUnionSet.{u3} α) s t)) (Sup.sup.{max u2 u3} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SemilatticeSup.toSup.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Lattice.toSemilatticeSup.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toLattice.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))))) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 t))
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (t : Set.{u3} α), Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (Union.union.{u3} (Set.{u3} α) (Set.instUnionSet.{u3} α) s t)) (Sup.sup.{max u2 u3} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SemilatticeSup.toSup.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Lattice.toSemilatticeSup.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toLattice.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))))) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 t))
Case conversion may be inaccurate. Consider using '#align finsupp.supported_union Finsupp.supported_unionₓ'. -/
theorem supported_union (s t : Set α) : supported M R (s ∪ t) = supported M R s ⊔ supported M R t :=
by erw [Set.union_eq_unionᵢ, supported_Union, supᵢ_bool_eq] <;> rfl
@@ -504,7 +504,7 @@ theorem supported_union (s t : Set α) : supported M R (s ∪ t) = supported M R
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {ι : Type.{u4}} (s : ι -> (Set.{u1} α)), Eq.{succ (max u1 u2)} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (Set.interᵢ.{u1, succ u4} α ι (fun (i : ι) => s i))) (infᵢ.{max u1 u2, succ u4} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasInf.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) ι (fun (i : ι) => Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (s i)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {ι : Type.{u4}} (s : ι -> (Set.{u3} α)), Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (Set.interᵢ.{u3, succ u4} α ι (fun (i : ι) => s i))) (infᵢ.{max u2 u3, succ u4} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) ι (fun (i : ι) => Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (s i)))
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {ι : Type.{u4}} (s : ι -> (Set.{u3} α)), Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (Set.interᵢ.{u3, succ u4} α ι (fun (i : ι) => s i))) (infᵢ.{max u2 u3, succ u4} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) ι (fun (i : ι) => Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (s i)))
Case conversion may be inaccurate. Consider using '#align finsupp.supported_Inter Finsupp.supported_interᵢₓ'. -/
theorem supported_interᵢ {ι : Type _} (s : ι → Set α) :
supported M R (⋂ i, s i) = ⨅ i, supported M R (s i) :=
@@ -515,7 +515,7 @@ theorem supported_interᵢ {ι : Type _} (s : ι → Set α) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α) (t : Set.{u1} α), Eq.{succ (max u1 u2)} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)) (Inf.inf.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasInf.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 t))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (t : Set.{u3} α), Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (Inter.inter.{u3} (Set.{u3} α) (Set.instInterSet.{u3} α) s t)) (Inf.inf.{max u2 u3} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instInfSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 t))
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (t : Set.{u3} α), Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (Inter.inter.{u3} (Set.{u3} α) (Set.instInterSet.{u3} α) s t)) (Inf.inf.{max u2 u3} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instInfSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 t))
Case conversion may be inaccurate. Consider using '#align finsupp.supported_inter Finsupp.supported_interₓ'. -/
theorem supported_inter (s t : Set α) : supported M R (s ∩ t) = supported M R s ⊓ supported M R t :=
by rw [Set.inter_eq_interᵢ, supported_Inter, infᵢ_bool_eq] <;> rfl
@@ -525,7 +525,7 @@ theorem supported_inter (s t : Set α) : supported M R (s ∩ t) = supported M R
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {s : Set.{u1} α} {t : Set.{u1} α}, (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) s t) -> (Disjoint.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) (Submodule.orderBot.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 t))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {s : Set.{u3} α} {t : Set.{u3} α}, (Disjoint.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} α) (Preorder.toLE.{u3} (Set.{u3} α) (PartialOrder.toPreorder.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) s t) -> (Disjoint.{max u2 u3} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 t))
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {s : Set.{u3} α} {t : Set.{u3} α}, (Disjoint.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} α) (Preorder.toLE.{u3} (Set.{u3} α) (PartialOrder.toPreorder.{u3} (Set.{u3} α) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} α) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} α) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} α) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} α) (Set.instCompleteBooleanAlgebraSet.{u3} α)))))) s t) -> (Disjoint.{max u2 u3} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 t))
Case conversion may be inaccurate. Consider using '#align finsupp.disjoint_supported_supported Finsupp.disjoint_supported_supportedₓ'. -/
theorem disjoint_supported_supported {s t : Set α} (h : Disjoint s t) :
Disjoint (supported M R s) (supported M R t) :=
@@ -536,7 +536,7 @@ theorem disjoint_supported_supported {s t : Set α} (h : Disjoint s t) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] [_inst_9 : Nontrivial.{u2} M] {s : Set.{u1} α} {t : Set.{u1} α}, Iff (Disjoint.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) (Submodule.orderBot.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 t)) (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) s t)
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u3}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u1, u3} R M _inst_1 _inst_3] [_inst_9 : Nontrivial.{u3} M] {s : Set.{u2} α} {t : Set.{u2} α}, Iff (Disjoint.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u2 u3} R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4)))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u1, max u2 u3} R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4 s) (Finsupp.supported.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4 t)) (Disjoint.{u2} (Set.{u2} α) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} α) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α)))))) (BoundedOrder.toOrderBot.{u2} (Set.{u2} α) (Preorder.toLE.{u2} (Set.{u2} α) (PartialOrder.toPreorder.{u2} (Set.{u2} α) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} α) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α)))))))) (CompleteLattice.toBoundedOrder.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α)))))) s t)
+ forall {α : Type.{u2}} {M : Type.{u3}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u1, u3} R M _inst_1 _inst_3] [_inst_9 : Nontrivial.{u3} M] {s : Set.{u2} α} {t : Set.{u2} α}, Iff (Disjoint.{max u3 u2} (Submodule.{u1, max u3 u2} R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) (Finsupp.module.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) (Finsupp.module.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u3} (Submodule.{u1, max u3 u2} R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) (Finsupp.module.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u2 u3} R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) (Finsupp.module.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4)))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u1, max u2 u3} R (Finsupp.{u2, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u2, u3} α M _inst_3) (Finsupp.module.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4 s) (Finsupp.supported.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4 t)) (Disjoint.{u2} (Set.{u2} α) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} α) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α)))))) (BoundedOrder.toOrderBot.{u2} (Set.{u2} α) (Preorder.toLE.{u2} (Set.{u2} α) (PartialOrder.toPreorder.{u2} (Set.{u2} α) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} α) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α)))))))) (CompleteLattice.toBoundedOrder.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α)))))) s t)
Case conversion may be inaccurate. Consider using '#align finsupp.disjoint_supported_supported_iff Finsupp.disjoint_supported_supported_iffₓ'. -/
theorem disjoint_supported_supported_iff [Nontrivial M] {s t : Set α} :
Disjoint (supported M R s) (supported M R t) ↔ Disjoint s t :=
@@ -552,7 +552,7 @@ theorem disjoint_supported_supported_iff [Nontrivial M] {s t : Set α} :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α), LinearEquiv.{u3, u3, max u1 u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.addCommMonoid.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.addCommMonoid.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) M _inst_3) (Submodule.module.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.module.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) M R _inst_1 _inst_3 _inst_4)
but is expected to have type
- forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α), LinearEquiv.{u3, u3, max u1 u2, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Subtype.{succ (max u1 u2)} (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u1 u2, max u1 u2} (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u3, max u2 u1} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u3, max u2 u1} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) x (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s))) (Finsupp.{u1, u2} (Set.Elem.{u1} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.addCommMonoid.{u1, u2} (Set.Elem.{u1} α s) M _inst_3) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u3} (Set.Elem.{u1} α s) M R _inst_1 _inst_3 _inst_4)
+ forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α), LinearEquiv.{u3, u3, max u1 u2, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Subtype.{succ (max u1 u2)} (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u1 u2, max u1 u2} (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u3, max u2 u1} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u3, max u2 u1} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) x (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s))) (Finsupp.{u1, u2} (Set.Elem.{u1} α s) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.addCommMonoid.{u1, u2} (Set.Elem.{u1} α s) M _inst_3) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.module.{u1, u2, u3} (Set.Elem.{u1} α s) M R _inst_1 _inst_3 _inst_4)
Case conversion may be inaccurate. Consider using '#align finsupp.supported_equiv_finsupp Finsupp.supportedEquivFinsuppₓ'. -/
/-- Interpret `finsupp.restrict_support_equiv` as a linear equivalence between
`supported M R s` and `s →₀ M`. -/
@@ -576,7 +576,7 @@ variable (S) [Module S N] [SMulCommClass R S N]
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toHasSmul.{u4, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u4, u3} R N (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u5, u3} S N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u5, u3} S N (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))], LinearEquiv.{u5, u5, max u1 u2 u3, max (max u1 u2) u3} S S _inst_2 _inst_2 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2) (α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u1, max u2 u3} α (fun (ᾰ : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.Function.module.{u1, u5, max u2 u3} α S (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.module.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.module.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)
but is expected to have type
- forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toSMul.{u4, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u4, u3} R N (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u5, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} S N (MonoidWithZero.toZero.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))], LinearEquiv.{u5, u5, max (max u1 u2) u3, max u3 u2 u1} S S _inst_2 _inst_2 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2) (α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u4, u4, max u2 u1, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u1, max u2 u3} α (fun (ᾰ : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.module.{u1, max u2 u3, u5} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)
+ forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toSMul.{u4, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u4, u3} R N (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u5, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} S N (MonoidWithZero.toZero.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))], LinearEquiv.{u5, u5, max (max u1 u2) u3, max u3 u2 u1} S S _inst_2 _inst_2 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2) (α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u4, u4, max u2 u1, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u1, max u2 u3} α (fun (ᾰ : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.module.{u1, max u2 u3, u5} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)
Case conversion may be inaccurate. Consider using '#align finsupp.lsum Finsupp.lsumₓ'. -/
/-- Lift a family of linear maps `M →ₗ[R] N` indexed by `x : α` to a linear map from `α →₀ M` to
`N` using `finsupp.sum`. This is an upgraded version of `finsupp.lift_add_hom`.
@@ -608,7 +608,7 @@ def lsum : (α → M →ₗ[R] N) ≃ₗ[S] (α →₀ M) →ₗ[R] N
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toHasSmul.{u4, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u4, u3} R N (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u5, u3} S N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u5, u3} S N (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)), Eq.{max (max (succ u1) (succ u2)) (succ u3)} ((fun (_x : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) => (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) -> N) (coeFn.{max (succ (max u1 u2 u3)) (succ (max (max u1 u2) u3)), max (succ (max u1 u2 u3)) (succ (max (max u1 u2) u3))} (LinearEquiv.{u5, u5, max u1 u2 u3, max (max u1 u2) u3} S S _inst_2 _inst_2 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S 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_inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6)) (LinearEquiv.hasCoeToFun.{u5, u5, max u1 u2 u3, max (max u1 u2) u3} S S (α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u1, max u2 u3} α (fun (ᾰ : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.Function.module.{u1, u5, max u2 u3} α S (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.module.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.module.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2)) (Finsupp.lsum.{u1, u2, u3, u4, u5} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f)) (fun (d : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) => Finsupp.sum.{u1, u2, u3} α M N (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_5 d (fun (i : α) => coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (_x : LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) => M -> N) (LinearMap.hasCoeToFun.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (f i)))
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u4}} {N : Type.{u3}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u3} R S N (SMulZeroClass.toSMul.{u5, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)), Eq.{max (max (succ u2) (succ u4)) (succ u3)} (forall (a : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) a) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) 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_inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (fun (_x : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _x) (SMulHomClass.toFunLike.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2} S S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f)) (fun (d : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => Finsupp.sum.{u2, u4, u3} α M ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) d) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) _inst_5 d (fun (i : α) => FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f i)))
+ forall {α : Type.{u2}} {M : Type.{u4}} {N : Type.{u3}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u3} R S N (SMulZeroClass.toSMul.{u5, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)), Eq.{max (max (succ u2) (succ u4)) (succ u3)} (forall (a : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) a) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) f) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (fun (_x : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (fun (_x : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _x) (SMulHomClass.toFunLike.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R 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_inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f i)))
Case conversion may be inaccurate. Consider using '#align finsupp.coe_lsum Finsupp.coe_lsumₓ'. -/
@[simp]
theorem coe_lsum (f : α → M →ₗ[R] N) : (lsum S f : (α →₀ M) → N) = fun d => d.Sum fun i => f i :=
@@ -619,7 +619,7 @@ theorem coe_lsum (f : α → M →ₗ[R] N) : (lsum S f : (α →₀ M) → N) =
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toHasSmul.{u4, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u4, u3} R N (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u5, u3} S N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u5, u3} S N (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (l : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))), Eq.{succ u3} N (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (fun (_x : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 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M N _inst_3 _inst_5 _inst_4 _inst_6)) -> (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6)) (LinearEquiv.hasCoeToFun.{u5, u5, max u1 u2 u3, max (max u1 u2) u3} S S (α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u1, max u2 u3} α (fun (ᾰ : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.Function.module.{u1, u5, max u2 u3} α S (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.module.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.module.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2)) (Finsupp.lsum.{u1, u2, u3, u4, u5} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f) l) (Finsupp.sum.{u1, u2, u3} α M N (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_5 l (fun (b : α) => coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (_x : LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) => M -> N) (LinearMap.hasCoeToFun.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (f b)))
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u4}} {N : Type.{u3}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u3} R S N (SMulZeroClass.toSMul.{u5, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (l : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) l) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), succ u3} ((fun 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(Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (fun (_x : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M 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_inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => 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(Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2} S S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f) l) (Finsupp.sum.{u2, u4, u3} α M N (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) _inst_5 l (fun (b : α) => FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f b)))
+ forall {α : Type.{u2}} {M : Type.{u4}} {N : Type.{u3}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u3} R S N (SMulZeroClass.toSMul.{u5, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (l : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) l) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) f) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (fun (_x : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (fun (_x : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _x) (SMulHomClass.toFunLike.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R 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_inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M 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Case conversion may be inaccurate. Consider using '#align finsupp.lsum_apply Finsupp.lsum_applyₓ'. -/
theorem lsum_apply (f : α → M →ₗ[R] N) (l : α →₀ M) : Finsupp.lsum S f l = l.Sum fun b => f b :=
rfl
@@ -629,7 +629,7 @@ theorem lsum_apply (f : α → M →ₗ[R] N) (l : α →₀ M) : Finsupp.lsum S
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toHasSmul.{u4, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u4, u3} R N (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u5, u3} S N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u5, u3} S N (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (i : α) (m : M), Eq.{succ u3} N (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (fun (_x : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) => (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M 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(Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.module.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.module.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2)) (Finsupp.lsum.{u1, u2, u3, u4, u5} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f) (Finsupp.single.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) i m)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (_x : LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) => M -> N) (LinearMap.hasCoeToFun.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (f i) m)
but is expected to have type
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(AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (i : α) (m : M), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) (Finsupp.single.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) i m)) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), succ u3} 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_inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (fun (_x : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M 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(a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => 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(Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2} S S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f) (Finsupp.single.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) i m)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f i) m)
+ forall {α : Type.{u2}} {M : Type.{u4}} {N : Type.{u3}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u3} R S N (SMulZeroClass.toSMul.{u5, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (i : α) (m : M), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) (Finsupp.single.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) i m)) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) f) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (fun (_x : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (fun (_x : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _x) (SMulHomClass.toFunLike.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M 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_inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.module.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f) (Finsupp.single.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) i m)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f i) m)
Case conversion may be inaccurate. Consider using '#align finsupp.lsum_single Finsupp.lsum_singleₓ'. -/
theorem lsum_single (f : α → M →ₗ[R] N) (i : α) (m : M) :
Finsupp.lsum S f (Finsupp.single i m) = f i m :=
@@ -640,7 +640,7 @@ theorem lsum_single (f : α → M →ₗ[R] N) (i : α) (m : M) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toHasSmul.{u4, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u4, u3} R N (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u5, u3} S N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u5, u3} S N (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))] (f : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (x : α), Eq.{max (succ u2) (succ u3)} (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (coeFn.{max (succ (max (max u1 u2) u3)) (succ (max u1 u2 u3)), max (succ (max (max u1 u2) u3)) (succ (max u1 u2 u3))} (LinearEquiv.{u5, u5, max (max u1 u2) u3, max u1 u2 u3} S S _inst_2 _inst_2 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2) (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.addCommMonoid.{u1, max u2 u3} α (fun (ᾰ : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => 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(AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.addCommMonoid.{u1, max u2 u3} α (fun (ᾰ : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.module.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 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(Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u1, max u2 u3} α (fun (ᾰ : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.Function.module.{u1, u5, max u2 u3} α S (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.module.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.module.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2) (Finsupp.lsum.{u1, u2, u3, u4, u5} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10)) f x) (LinearMap.comp.{u4, u4, u4, u2, max u1 u2, u3} R R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 _inst_4 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomCompTriple.right_ids.{u4, u4} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) f (Finsupp.lsingle.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4 x))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u4}} {N : Type.{u2}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : Module.{u5, u2} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u2} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u2} R S N (SMulZeroClass.toSMul.{u5, u2} R N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u2} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u2} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (Module.toMulActionWithZero.{u5, u2} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u2} S N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u2} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u2} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (Module.toMulActionWithZero.{u1, u2} S N _inst_2 _inst_5 _inst_9))))] (f : LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (x : α), Eq.{max (succ u4) (succ u2)} (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (max (succ u2) (succ u4)) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (fun (_x : LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) => α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _x) (SMulHomClass.toFunLike.{max (max u2 u4) u3, u1, max (max u2 u4) u3, max (max u2 u4) u3} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (SMulZeroClass.toSMul.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (SMulZeroClass.toSMul.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u4) u3, u1, max (max u2 u4) u3, max (max u2 u4) u3} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u2 u4) u3, max (max u2 u4) u3, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M 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(Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) _inst_2 _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (LinearEquiv.symm.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (ᾰ : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (Finsupp.lsum.{u3, u4, u2, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10)) f x) (LinearMap.comp.{u5, u5, u5, u4, max u3 u4, u2} R R R M (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 _inst_4 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHomCompTriple.ids.{u5, u5} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) f (Finsupp.lsingle.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4 x))
+ forall {α : Type.{u3}} {M : Type.{u4}} {N : Type.{u2}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : Module.{u5, u2} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u2} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u2} R S N (SMulZeroClass.toSMul.{u5, u2} R N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u2} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u2} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (Module.toMulActionWithZero.{u5, u2} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u2} S N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u2} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u2} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (Module.toMulActionWithZero.{u1, u2} S N _inst_2 _inst_5 _inst_9))))] (f : LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (x : α), Eq.{max (succ u4) (succ u2)} (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (max (succ u2) (succ u4)) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (fun (_x : LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) => α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _x) (SMulHomClass.toFunLike.{max (max u2 u4) u3, u1, max (max u2 u4) u3, max (max u2 u4) u3} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (SMulZeroClass.toSMul.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (SMulZeroClass.toSMul.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u4) u3, u1, max (max u2 u4) u3, max (max u2 u4) u3} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u2 u4) u3, max (max u2 u4) u3, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α 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_inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R 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u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) _inst_2 _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (LinearEquiv.symm.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (ᾰ : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (Finsupp.lsum.{u3, u4, u2, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10)) f x) (LinearMap.comp.{u5, u5, u5, u4, max u3 u4, u2} R R R M (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 _inst_4 (Finsupp.module.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHomCompTriple.ids.{u5, u5} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) f (Finsupp.lsingle.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4 x))
Case conversion may be inaccurate. Consider using '#align finsupp.lsum_symm_apply Finsupp.lsum_symm_applyₓ'. -/
theorem lsum_symm_apply (f : (α →₀ M) →ₗ[R] N) (x : α) : (lsum S).symm f x = f.comp (lsingle x) :=
rfl
@@ -656,7 +656,7 @@ variable (M) (R) (X : Type _)
lean 3 declaration is
forall (M : Type.{u1}) (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u3}), AddEquiv.{max u3 u1, max (max u3 u2) u1} (X -> M) (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (ᾰ : X) => M) (fun (i : X) => AddZeroClass.toHasAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.hasAdd.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))
but is expected to have type
- forall (M : Type.{u1}) (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u3}), AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (ᾰ : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))
+ forall (M : Type.{u1}) (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u3}), AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (ᾰ : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))
Case conversion may be inaccurate. Consider using '#align finsupp.lift Finsupp.liftₓ'. -/
/-- A slight rearrangement from `lsum` gives us
the bijection underlying the free-forgetful adjunction for R-modules.
@@ -670,7 +670,7 @@ noncomputable def lift : (X → M) ≃+ ((X →₀ R) →ₗ[R] M) :=
lean 3 declaration is
forall (M : Type.{u1}) (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u3}) (f : LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (x : X), Eq.{succ u1} M (coeFn.{max (succ (max (max u3 u2) u1)) (succ (max u3 u1)), max (succ (max (max u3 u2) u1)) (succ (max u3 u1))} (AddEquiv.{max (max u3 u2) u1, max u3 u1} (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (X -> M) (LinearMap.hasAdd.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R 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(Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (X -> M) (LinearMap.hasAdd.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} 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(MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) => (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R 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(NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))))))
but is expected to have type
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R 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(RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (AddZeroClass.toAdd.{max u1 u2} (X -> M) (Pi.addZeroClass.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (AddMonoidHomClass.toAddHomClass.{max (max u1 u3) u2, max (max u1 u3) u2, max u1 u2} (AddEquiv.{max (max u1 u3) u2, max u1 u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (LinearMap.instAddLinearMap.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R 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(MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Pi.addZeroClass.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddEquivClass.instAddMonoidHomClass.{max (max u1 u3) u2, max (max u1 u3) u2, max u1 u2} (AddEquiv.{max (max u1 u3) u2, max u1 u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (LinearMap.instAddLinearMap.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.instAdd.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (AddMonoid.toAddZeroClass.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R 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X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (fun (_x : Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (LinearMap.instAddLinearMap.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) 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Case conversion may be inaccurate. Consider using '#align finsupp.lift_symm_apply Finsupp.lift_symm_applyₓ'. -/
@[simp]
theorem lift_symm_apply (f) (x) : ((lift M R X).symm f) x = f (single x 1) :=
@@ -681,7 +681,7 @@ theorem lift_symm_apply (f) (x) : ((lift M R X).symm f) x = f (single x 1) :=
lean 3 declaration is
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(AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4)))) r (f x)))
but is expected to have type
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(AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddEquiv.instAddEquivClassAddEquiv.{max u1 u3, max (max u1 u2) u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (Finsupp.lift.{u1, u2, u3} M R _inst_1 _inst_3 _inst_4 X) f) g) (Finsupp.sum.{u3, u2, u1} X R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) _inst_3 g (fun (x : X) (r : R) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4))))) r (f x)))
+ forall (M : Type.{u1}) (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u3}) (f : X -> M) (g : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) g) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : X -> M) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) f) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (max (succ u1) (succ u2)) (succ u3)} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (fun (_x : X -> M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : X -> M) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) _x) (AddHomClass.toFunLike.{max (max u1 u2) u3, max u1 u3, max (max u1 u2) u3} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddZeroClass.toAdd.{max u1 u3} (X -> M) (Pi.addZeroClass.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (AddZeroClass.toAdd.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (AddMonoidHomClass.toAddHomClass.{max (max u1 u2) u3, max u1 u3, max (max u1 u2) u3} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.addZeroClass.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddEquivClass.instAddMonoidHomClass.{max (max u1 u2) u3, max u1 u3, max (max u1 u2) u3} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.addZeroClass.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddEquiv.instAddEquivClassAddEquiv.{max u1 u3, max (max u1 u2) u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (Finsupp.lift.{u1, u2, u3} M R _inst_1 _inst_3 _inst_4 X) f) g) (Finsupp.sum.{u3, u2, u1} X R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) _inst_3 g (fun (x : X) (r : R) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4))))) r (f x)))
Case conversion may be inaccurate. Consider using '#align finsupp.lift_apply Finsupp.lift_applyₓ'. -/
@[simp]
theorem lift_apply (f) (g) : ((lift M R X) f) g = g.Sum fun x r => r • f x :=
@@ -698,7 +698,7 @@ variable {α' : Type _} {α'' : Type _} (M R)
lean 3 declaration is
forall {α : Type.{u1}} (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {α' : Type.{u4}}, (α -> α') -> (LinearMap.{u3, u3, max u1 u2, max u4 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4))
but is expected to have type
- forall {α : Type.{u1}} (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {α' : Type.{u4}}, (α -> α') -> (LinearMap.{u3, u3, max u2 u1, max u2 u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4))
+ forall {α : Type.{u1}} (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {α' : Type.{u4}}, (α -> α') -> (LinearMap.{u3, u3, max u2 u1, max u2 u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4))
Case conversion may be inaccurate. Consider using '#align finsupp.lmap_domain Finsupp.lmapDomainₓ'. -/
/-- Interpret `finsupp.map_domain` as a linear map. -/
def lmapDomain (f : α → α') : (α →₀ M) →ₗ[R] α' →₀ M
@@ -712,7 +712,7 @@ def lmapDomain (f : α → α') : (α →₀ M) →ₗ[R] α' →₀ M
lean 3 declaration is
forall {α : Type.{u1}} (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {α' : Type.{u4}} (f : α -> α') (l : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))), Eq.{max (succ u4) (succ u2)} (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (coeFn.{max (succ (max u1 u2)) (succ (max u4 u2)), max (succ (max u1 u2)) (succ (max u4 u2))} (LinearMap.{u3, u3, max u1 u2, max u4 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4)) (fun (_x : LinearMap.{u3, u3, max u1 u2, max u4 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4)) => (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) -> (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))))) (LinearMap.hasCoeToFun.{u3, u3, max u1 u2, max u4 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lmapDomain.{u1, u2, u3, u4} α M R _inst_1 _inst_3 _inst_4 α' f) l) (Finsupp.mapDomain.{u1, u4, u2} α α' M _inst_3 f l)
but is expected to have type
- forall {α : Type.{u4}} (M : Type.{u3}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u1, u3} R M _inst_1 _inst_3] {α' : Type.{u2}} (f : α -> α') (l : Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) l) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u3), max (succ u3) (succ u2)} (LinearMap.{u1, u1, max u3 u4, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.addCommMonoid.{u4, u3} α M _inst_3) (Finsupp.addCommMonoid.{u2, u3} α' M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u3, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u1} α' M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (fun (_x : Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max u3 u2} R R (Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} α M _inst_3) (Finsupp.addCommMonoid.{u2, u3} α' M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u3, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lmapDomain.{u4, u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 α' f) l) (Finsupp.mapDomain.{u4, u2, u3} α α' M _inst_3 f l)
+ forall {α : Type.{u4}} (M : Type.{u3}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u1, u3} R M _inst_1 _inst_3] {α' : Type.{u2}} (f : α -> α') (l : Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) l) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u3), max (succ u3) (succ u2)} (LinearMap.{u1, u1, max u3 u4, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.addCommMonoid.{u4, u3} α M _inst_3) (Finsupp.addCommMonoid.{u2, u3} α' M _inst_3) (Finsupp.module.{u4, u3, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u2, u3, u1} α' M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (fun (_x : Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) => Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max u3 u2} R R (Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} α M _inst_3) (Finsupp.addCommMonoid.{u2, u3} α' M _inst_3) (Finsupp.module.{u4, u3, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u2, u3, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lmapDomain.{u4, u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 α' f) l) (Finsupp.mapDomain.{u4, u2, u3} α α' M _inst_3 f l)
Case conversion may be inaccurate. Consider using '#align finsupp.lmap_domain_apply Finsupp.lmapDomain_applyₓ'. -/
@[simp]
theorem lmapDomain_apply (f : α → α') (l : α →₀ M) :
@@ -724,7 +724,7 @@ theorem lmapDomain_apply (f : α → α') (l : α →₀ M) :
lean 3 declaration is
forall {α : Type.{u1}} (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], Eq.{succ (max u1 u2)} (LinearMap.{u3, u3, max u1 u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.lmapDomain.{u1, u2, u3, u1} α M R _inst_1 _inst_3 _inst_4 α (id.{succ u1} α)) (LinearMap.id.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))
but is expected to have type
- forall {α : Type.{u3}} (M : Type.{u2}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Eq.{max (succ u3) (succ u2)} (LinearMap.{u1, u1, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.lmapDomain.{u3, u2, u1, u3} α M R _inst_1 _inst_3 _inst_4 α (id.{succ u3} α)) (LinearMap.id.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))
+ forall {α : Type.{u3}} (M : Type.{u2}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Eq.{max (succ u3) (succ u2)} (LinearMap.{u1, u1, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.lmapDomain.{u3, u2, u1, u3} α M R _inst_1 _inst_3 _inst_4 α (id.{succ u3} α)) (LinearMap.id.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))
Case conversion may be inaccurate. Consider using '#align finsupp.lmap_domain_id Finsupp.lmapDomain_idₓ'. -/
@[simp]
theorem lmapDomain_id : (lmapDomain M R id : (α →₀ M) →ₗ[R] α →₀ M) = LinearMap.id :=
@@ -735,7 +735,7 @@ theorem lmapDomain_id : (lmapDomain M R id : (α →₀ M) →ₗ[R] α →₀ M
lean 3 declaration is
forall {α : Type.{u1}} (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {α' : Type.{u4}} {α'' : Type.{u5}} (f : α -> α') (g : α' -> α''), Eq.{max (succ (max u1 u2)) (succ (max u5 u2))} (LinearMap.{u3, u3, max u1 u2, max u5 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u5, u2} α'' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u5, u2} α'' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u5, u2, u3} α'' M R _inst_1 _inst_3 _inst_4)) (Finsupp.lmapDomain.{u1, u2, u3, u5} α M R _inst_1 _inst_3 _inst_4 α'' (Function.comp.{succ u1, succ u4, succ u5} α α' α'' g f)) (LinearMap.comp.{u3, u3, u3, max u1 u2, max u4 u2, max u5 u2} R R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u5, u2} α'' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.addCommMonoid.{u5, u2} α'' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u5, u2, u3} α'' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomCompTriple.right_ids.{u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lmapDomain.{u4, u2, u3, u5} α' M R _inst_1 _inst_3 _inst_4 α'' g) (Finsupp.lmapDomain.{u1, u2, u3, u4} α M R _inst_1 _inst_3 _inst_4 α' f))
but is expected to have type
- forall {α : Type.{u5}} (M : Type.{u4}) (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_1 _inst_3] {α' : Type.{u1}} {α'' : Type.{u3}} (f : α -> α') (g : α' -> α''), Eq.{max (max (succ u5) (succ u4)) (succ u3)} (LinearMap.{u2, u2, max u4 u5, max u4 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u5, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (Finsupp.{u3, u4} α'' M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (Finsupp.addCommMonoid.{u5, u4} α M _inst_3) (Finsupp.addCommMonoid.{u3, u4} α'' M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u5, u4, u2} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u2} α'' M R _inst_1 _inst_3 _inst_4)) (Finsupp.lmapDomain.{u5, u4, u2, u3} α M R _inst_1 _inst_3 _inst_4 α'' (Function.comp.{succ u5, succ u1, succ u3} α α' α'' g f)) (LinearMap.comp.{u2, u2, u2, max u4 u5, max u4 u1, max u4 u3} R R R (Finsupp.{u5, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (Finsupp.{u1, u4} α' M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (Finsupp.{u3, u4} α'' M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u5, u4} α M _inst_3) (Finsupp.addCommMonoid.{u1, u4} α' M _inst_3) (Finsupp.addCommMonoid.{u3, u4} α'' M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u5, u4, u2} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u4, u2} α' M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u2} α'' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.lmapDomain.{u1, u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4 α'' g) (Finsupp.lmapDomain.{u5, u4, u2, u1} α M R _inst_1 _inst_3 _inst_4 α' f))
+ forall {α : Type.{u5}} (M : Type.{u4}) (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_1 _inst_3] {α' : Type.{u1}} {α'' : Type.{u3}} (f : α -> α') (g : α' -> α''), Eq.{max (max (succ u5) (succ u4)) (succ u3)} (LinearMap.{u2, u2, max u4 u5, max u4 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u5, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (Finsupp.{u3, u4} α'' M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (Finsupp.addCommMonoid.{u5, u4} α M _inst_3) (Finsupp.addCommMonoid.{u3, u4} α'' M _inst_3) (Finsupp.module.{u5, u4, u2} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u4, u2} α'' M R _inst_1 _inst_3 _inst_4)) (Finsupp.lmapDomain.{u5, u4, u2, u3} α M R _inst_1 _inst_3 _inst_4 α'' (Function.comp.{succ u5, succ u1, succ u3} α α' α'' g f)) (LinearMap.comp.{u2, u2, u2, max u4 u5, max u4 u1, max u4 u3} R R R (Finsupp.{u5, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (Finsupp.{u1, u4} α' M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (Finsupp.{u3, u4} α'' M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u5, u4} α M _inst_3) (Finsupp.addCommMonoid.{u1, u4} α' M _inst_3) (Finsupp.addCommMonoid.{u3, u4} α'' M _inst_3) (Finsupp.module.{u5, u4, u2} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u4, u2} α' M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u4, u2} α'' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.lmapDomain.{u1, u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4 α'' g) (Finsupp.lmapDomain.{u5, u4, u2, u1} α M R _inst_1 _inst_3 _inst_4 α' f))
Case conversion may be inaccurate. Consider using '#align finsupp.lmap_domain_comp Finsupp.lmapDomain_compₓ'. -/
theorem lmapDomain_comp (f : α → α') (g : α' → α'') :
lmapDomain M R (g ∘ f) = (lmapDomain M R g).comp (lmapDomain M R f) :=
@@ -746,7 +746,7 @@ theorem lmapDomain_comp (f : α → α') (g : α' → α'') :
lean 3 declaration is
forall {α : Type.{u1}} (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {α' : Type.{u4}} (f : α -> α') (s : Set.{u4} α'), LE.le.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toLE.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))))) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (Set.preimage.{u1, u4} α α' f s)) (Submodule.comap.{u3, u3, max u1 u2, max u4 u2, max (max u1 u2) u4 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, max u1 u2, max u4 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u3, u3, max u1 u2, max u4 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lmapDomain.{u1, u2, u3, u4} α M R _inst_1 _inst_3 _inst_4 α' f) (Finsupp.supported.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4 s))
but is expected to have type
- forall {α : Type.{u3}} (M : Type.{u2}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {α' : Type.{u4}} (f : α -> α') (s : Set.{u4} α'), LE.le.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toLE.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))))) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (Set.preimage.{u3, u4} α α' f s)) (Submodule.comap.{u1, u1, max u3 u2, max u2 u4, max (max u2 u4) u3} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, max u2 u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u1} α' M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u3 u2, max u2 u4} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lmapDomain.{u3, u2, u1, u4} α M R _inst_1 _inst_3 _inst_4 α' f) (Finsupp.supported.{u4, u2, u1} α' M R _inst_1 _inst_3 _inst_4 s))
+ forall {α : Type.{u3}} (M : Type.{u2}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {α' : Type.{u4}} (f : α -> α') (s : Set.{u4} α'), LE.le.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Preorder.toLE.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (PartialOrder.toPreorder.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))))) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (Set.preimage.{u3, u4} α α' f s)) (Submodule.comap.{u1, u1, max u3 u2, max u2 u4, max (max u2 u4) u3} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, max u2 u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u1} α' M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u3 u2, max u2 u4} R R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lmapDomain.{u3, u2, u1, u4} α M R _inst_1 _inst_3 _inst_4 α' f) (Finsupp.supported.{u4, u2, u1} α' M R _inst_1 _inst_3 _inst_4 s))
Case conversion may be inaccurate. Consider using '#align finsupp.supported_comap_lmap_domain Finsupp.supported_comap_lmapDomainₓ'. -/
theorem supported_comap_lmapDomain (f : α → α') (s : Set α') :
supported M R (f ⁻¹' s) ≤ (supported M R s).comap (lmapDomain M R f) :=
@@ -761,7 +761,7 @@ theorem supported_comap_lmapDomain (f : α → α') (s : Set α') :
lean 3 declaration is
forall {α : Type.{u1}} (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {α' : Type.{u4}} [_inst_9 : Nonempty.{succ u1} α] (f : α -> α') (s : Set.{u1} α), Eq.{succ (max u4 u2)} (Submodule.{u3, max u4 u2} R (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4)) (Submodule.map.{u3, u3, max u1 u2, max u4 u2, max (max u1 u2) u4 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomSurjective.ids.{u3} R _inst_1) (LinearMap.{u3, u3, max u1 u2, max u4 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u3, u3, max u1 u2, max u4 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lmapDomain.{u1, u2, u3, u4} α M R _inst_1 _inst_3 _inst_4 α' f) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.supported.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4 (Set.image.{u1, u4} α α' f s))
but is expected to have type
- forall {α : Type.{u4}} (M : Type.{u3}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u1, u3} R M _inst_1 _inst_3] {α' : Type.{u2}} [_inst_9 : Nonempty.{succ u4} α] (f : α -> α') (s : Set.{u4} α), Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u3 u2} R (Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u2, u3} α' M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u1} α' M R _inst_1 _inst_3 _inst_4)) (Submodule.map.{u1, u1, max u4 u3, max u3 u2, max (max u3 u2) u4} R R (Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} α M _inst_3) (Finsupp.addCommMonoid.{u2, u3} α' M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u3, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.{u1, u1, max u3 u4, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.addCommMonoid.{u4, u3} α M _inst_3) (Finsupp.addCommMonoid.{u2, u3} α' M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u3, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u1} α' M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u4 u3, max u3 u2} R R (Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} α M _inst_3) (Finsupp.addCommMonoid.{u2, u3} α' M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u3, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lmapDomain.{u4, u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 α' f) (Finsupp.supported.{u4, u3, u1} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.supported.{u2, u3, u1} α' M R _inst_1 _inst_3 _inst_4 (Set.image.{u4, u2} α α' f s))
+ forall {α : Type.{u4}} (M : Type.{u3}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u1, u3} R M _inst_1 _inst_3] {α' : Type.{u2}} [_inst_9 : Nonempty.{succ u4} α] (f : α -> α') (s : Set.{u4} α), Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u3 u2} R (Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u2, u3} α' M _inst_3) (Finsupp.module.{u2, u3, u1} α' M R _inst_1 _inst_3 _inst_4)) (Submodule.map.{u1, u1, max u4 u3, max u3 u2, max (max u3 u2) u4} R R (Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} α M _inst_3) (Finsupp.addCommMonoid.{u2, u3} α' M _inst_3) (Finsupp.module.{u4, u3, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u2, u3, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.{u1, u1, max u3 u4, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.addCommMonoid.{u4, u3} α M _inst_3) (Finsupp.addCommMonoid.{u2, u3} α' M _inst_3) (Finsupp.module.{u4, u3, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u2, u3, u1} α' M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u4 u3, max u3 u2} R R (Finsupp.{u4, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u2, u3} α' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} α M _inst_3) (Finsupp.addCommMonoid.{u2, u3} α' M _inst_3) (Finsupp.module.{u4, u3, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u2, u3, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lmapDomain.{u4, u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 α' f) (Finsupp.supported.{u4, u3, u1} α M R _inst_1 _inst_3 _inst_4 s)) (Finsupp.supported.{u2, u3, u1} α' M R _inst_1 _inst_3 _inst_4 (Set.image.{u4, u2} α α' f s))
Case conversion may be inaccurate. Consider using '#align finsupp.lmap_domain_supported Finsupp.lmapDomain_supportedₓ'. -/
theorem lmapDomain_supported [Nonempty α] (f : α → α') (s : Set α) :
(supported M R s).map (lmapDomain M R f) = supported M R (f '' s) :=
@@ -786,7 +786,7 @@ theorem lmapDomain_supported [Nonempty α] (f : α → α') (s : Set α) :
lean 3 declaration is
forall {α : Type.{u1}} (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {α' : Type.{u4}} (f : α -> α') {s : Set.{u1} α}, (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (Eq.{succ u4} α' (f a) (f b)) -> (Eq.{succ u1} α a b))) -> (Disjoint.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) (Submodule.orderBot.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s) (LinearMap.ker.{u3, u3, max u1 u2, max u4 u2, max (max u1 u2) u4 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, max u1 u2, max u4 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4)) (LinearMap.semilinearMapClass.{u3, u3, max u1 u2, max u4 u2} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.lmapDomain.{u1, u2, u3, u4} α M R _inst_1 _inst_3 _inst_4 α' f)))
but is expected to have type
- forall {α : Type.{u4}} (M : Type.{u2}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {α' : Type.{u3}} (f : α -> α') {s : Set.{u4} α}, (forall (a : α), (Membership.mem.{u4, u4} α (Set.{u4} α) (Set.instMembershipSet.{u4} α) a s) -> (forall (b : α), (Membership.mem.{u4, u4} α (Set.{u4} α) (Set.instMembershipSet.{u4} α) b s) -> (Eq.{succ u3} α' (f a) (f b)) -> (Eq.{succ u4} α a b))) -> (Disjoint.{max u2 u4} (Submodule.{u1, max u2 u4} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u4 u2} (Submodule.{u1, max u2 u4} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u4 u2} (Submodule.{u1, max u2 u4} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u4 u2} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u1, max u4 u2} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) (LinearMap.ker.{u1, u1, max u4 u2, max u2 u3, max (max u2 u3) u4} R R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α' M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u4, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α' M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α' M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u4 u2, max u2 u3} R R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α' M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lmapDomain.{u4, u2, u1, u3} α M R _inst_1 _inst_3 _inst_4 α' f)))
+ forall {α : Type.{u4}} (M : Type.{u2}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {α' : Type.{u3}} (f : α -> α') {s : Set.{u4} α}, (forall (a : α), (Membership.mem.{u4, u4} α (Set.{u4} α) (Set.instMembershipSet.{u4} α) a s) -> (forall (b : α), (Membership.mem.{u4, u4} α (Set.{u4} α) (Set.instMembershipSet.{u4} α) b s) -> (Eq.{succ u3} α' (f a) (f b)) -> (Eq.{succ u4} α a b))) -> (Disjoint.{max u2 u4} (Submodule.{u1, max u2 u4} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u4 u2} (Submodule.{u1, max u2 u4} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u4 u2} (Submodule.{u1, max u2 u4} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u4 u2} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u1, max u4 u2} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) (LinearMap.ker.{u1, u1, max u4 u2, max u2 u3, max (max u2 u3) u4} R R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u4, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α' M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u4 u2, max u2 u3} R R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lmapDomain.{u4, u2, u1, u3} α M R _inst_1 _inst_3 _inst_4 α' f)))
Case conversion may be inaccurate. Consider using '#align finsupp.lmap_domain_disjoint_ker Finsupp.lmapDomain_disjoint_kerₓ'. -/
/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a b «expr ∈ » s) -/
theorem lmapDomain_disjoint_ker (f : α → α') {s : Set α}
@@ -822,7 +822,7 @@ variable {β : Type _} {R M}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {β : Type.{u4}} (f : α -> β), (Function.Injective.{succ u1, succ u4} α β f) -> (LinearMap.{u3, u3, max u4 u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u2} β M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.addCommMonoid.{u4, u2} β M _inst_3) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u4, u2, u3} β M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))
but is expected to have type
- forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {β : Type.{u4}} (f : α -> β), (Function.Injective.{succ u1, succ u4} α β f) -> (LinearMap.{u3, u3, max u2 u4, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} β M _inst_3) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u3} β M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))
+ forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {β : Type.{u4}} (f : α -> β), (Function.Injective.{succ u1, succ u4} α β f) -> (LinearMap.{u3, u3, max u2 u4, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} β M _inst_3) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u4, u2, u3} β M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))
Case conversion may be inaccurate. Consider using '#align finsupp.lcomap_domain Finsupp.lcomapDomainₓ'. -/
/-- Given `f : α → β` and a proof `hf` that `f` is injective, `lcomap_domain f hf` is the linear map
sending `l : β →₀ M` to the finitely supported function from `α` to `M` given by composing
@@ -851,7 +851,7 @@ variable (α) {α' : Type _} (M) {M' : Type _} (R) [AddCommMonoid M'] [Module R
lean 3 declaration is
forall (α : Type.{u1}) (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], (α -> M) -> (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4)
but is expected to have type
- forall (α : Type.{u1}) (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], (α -> M) -> (LinearMap.{u3, u3, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4)
+ forall (α : Type.{u1}) (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], (α -> M) -> (LinearMap.{u3, u3, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4)
Case conversion may be inaccurate. Consider using '#align finsupp.total Finsupp.totalₓ'. -/
/-- Interprets (l : α →₀ R) as linear combination of the elements in the family (v : α → M) and
evaluates this linear combination. -/
@@ -865,7 +865,7 @@ variable {α M v}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {v : α -> M} (l : Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v) l) (Finsupp.sum.{u1, u3, u2} α R M (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 l (fun (i : α) (a : R) => SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) a (v i)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {v : α -> M} (l : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 v) l) (Finsupp.sum.{u3, u2, u1} α R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) _inst_3 l (fun (i : α) (a : R) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4))))) a (v i)))
+ forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {v : α -> M} (l : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 v) l) (Finsupp.sum.{u3, u2, u1} α R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) _inst_3 l (fun (i : α) (a : R) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4))))) a (v i)))
Case conversion may be inaccurate. Consider using '#align finsupp.total_apply Finsupp.total_applyₓ'. -/
theorem total_apply (l : α →₀ R) : Finsupp.total α M R v l = l.Sum fun i a => a • v i :=
rfl
@@ -873,9 +873,9 @@ theorem total_apply (l : α →₀ R) : Finsupp.total α M R v l = l.Sum fun i a
/- warning: finsupp.total_apply_of_mem_supported -> Finsupp.total_apply_of_mem_supported is a dubious translation:
lean 3 declaration is
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (SetLike.hasMem.{max u1 u3, max u1 u3} (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v) l) (Finset.sum.{u2, u1} M α _inst_3 s (fun (i : α) => SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M 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but is expected to have type
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R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1) (Finset.toSet.{u3} α s))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 v) l) (Finset.sum.{u1, u3} M α _inst_3 s (fun (i : α) => HSMul.hSMul.{u2, u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M M (instHSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (SMulZeroClass.toSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M _inst_1 _inst_3 _inst_4))))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) α (fun (_x : α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) _x) (Finsupp.funLike.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) l i) (v i))))
+ forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {v : α -> M} {l : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))} {s : Finset.{u3} α}, (Membership.mem.{max u3 u2, max u2 u3} (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (Submodule.instSetLikeSubmodule.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)))) l (Finsupp.supported.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1) (Finset.toSet.{u3} α s))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 v) l) (Finset.sum.{u1, u3} M α _inst_3 s (fun (i : α) => HSMul.hSMul.{u2, u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M M (instHSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (SMulZeroClass.toSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) i) M _inst_1 _inst_3 _inst_4))))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) α (fun (_x : α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) _x) (Finsupp.funLike.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) l i) (v i))))
Case conversion may be inaccurate. Consider using '#align finsupp.total_apply_of_mem_supported Finsupp.total_apply_of_mem_supportedₓ'. -/
theorem total_apply_of_mem_supported {l : α →₀ R} {s : Finset α}
(hs : l ∈ supported R R (↑s : Set α)) : Finsupp.total α M R v l = s.Sum fun i => l i • v i :=
@@ -887,7 +887,7 @@ theorem total_apply_of_mem_supported {l : α →₀ R} {s : Finset α}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {v : α -> M} (c : R) (a : α), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v) (Finsupp.single.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) a c)) (SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) c (v a))
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u3}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u1, u3} R M _inst_1 _inst_3] {v : α -> M} (c : R) (a : α), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) (Finsupp.single.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) a c)) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u1), succ u3} (LinearMap.{u1, u1, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u3} R R (Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4 v) (Finsupp.single.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) a c)) (HSMul.hSMul.{u1, u3, u3} R M M (instHSMul.{u1, u3} R M (SMulZeroClass.toSMul.{u1, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u1, u3} R M _inst_1 _inst_3 _inst_4))))) c (v a))
+ forall {α : Type.{u2}} {M : Type.{u3}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u1, u3} R M _inst_1 _inst_3] {v : α -> M} (c : R) (a : α), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) (Finsupp.single.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) a c)) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u1), succ u3} (LinearMap.{u1, u1, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u3} R R (Finsupp.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u3, u1} α M R _inst_1 _inst_3 _inst_4 v) (Finsupp.single.{u2, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) a c)) (HSMul.hSMul.{u1, u3, u3} R M M (instHSMul.{u1, u3} R M (SMulZeroClass.toSMul.{u1, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u1, u3} R M _inst_1 _inst_3 _inst_4))))) c (v a))
Case conversion may be inaccurate. Consider using '#align finsupp.total_single Finsupp.total_singleₓ'. -/
@[simp]
theorem total_single (c : R) (a : α) : Finsupp.total α M R v (single a c) = c • v a := by
@@ -898,7 +898,7 @@ theorem total_single (c : R) (a : α) : Finsupp.total α M R v (single a c) = c
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (x : Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u1 u2} (α -> M) 0 (OfNat.mk.{max u1 u2} (α -> M) 0 (Zero.zero.{max u1 u2} (α -> M) (Pi.instZero.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))))))) x) (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))))))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u3 u1} (α -> M) 0 (Zero.toOfNat0.{max u3 u1} (α -> M) (Pi.instZero.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.6475 : α) => M) (fun (i : α) => AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) _inst_3))))
+ forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u3 u1} (α -> M) 0 (Zero.toOfNat0.{max u3 u1} (α -> M) (Pi.instZero.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.6475 : α) => M) (fun (i : α) => AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) _inst_3))))
Case conversion may be inaccurate. Consider using '#align finsupp.total_zero_apply Finsupp.total_zero_applyₓ'. -/
theorem total_zero_apply (x : α →₀ R) : (Finsupp.total α M R 0) x = 0 := by
simp [Finsupp.total_apply]
@@ -910,7 +910,7 @@ variable (α M)
lean 3 declaration is
forall (α : Type.{u1}) (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], Eq.{max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u1 u2} (α -> M) 0 (OfNat.mk.{max u1 u2} (α -> M) 0 (Zero.zero.{max u1 u2} (α -> M) (Pi.instZero.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))))))) (OfNat.ofNat.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) 0 (OfNat.mk.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) 0 (Zero.zero.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.hasZero.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))
but is expected to have type
- forall (α : Type.{u3}) (M : Type.{u2}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Eq.{max (max (succ u3) (succ u2)) (succ u1)} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u3 u2} (α -> M) 0 (Zero.toOfNat0.{max u3 u2} (α -> M) (Pi.instZero.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.6475 : α) => M) (fun (i : α) => AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))))) (OfNat.ofNat.{max (max u3 u2) u1} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) 0 (Zero.toOfNat0.{max (max u3 u2) u1} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (LinearMap.instZeroLinearMap.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))
+ forall (α : Type.{u3}) (M : Type.{u2}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Eq.{max (max (succ u3) (succ u2)) (succ u1)} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u3 u2} (α -> M) 0 (Zero.toOfNat0.{max u3 u2} (α -> M) (Pi.instZero.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.6475 : α) => M) (fun (i : α) => AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))))) (OfNat.ofNat.{max (max u3 u2) u1} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) 0 (Zero.toOfNat0.{max (max u3 u2) u1} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (LinearMap.instZeroLinearMap.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))
Case conversion may be inaccurate. Consider using '#align finsupp.total_zero Finsupp.total_zeroₓ'. -/
@[simp]
theorem total_zero : Finsupp.total α M R 0 = 0 :=
@@ -923,7 +923,7 @@ variable {α M}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {M' : Type.{u4}} [_inst_9 : AddCommMonoid.{u4} M'] [_inst_10 : Module.{u3, u4} R M' _inst_1 _inst_9] (f : LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_3 _inst_9 _inst_4 _inst_10) (v : α -> M) (l : Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))), Eq.{succ u4} M' (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_3 _inst_9 _inst_4 _inst_10) (fun (_x : LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' 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but is expected to have type
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(x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, u2} R R M _inst_1 _inst_3 _inst_3 M' _inst_4 _inst_10 _inst_9 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_3))) f) v)) l)
Case conversion may be inaccurate. Consider using '#align finsupp.apply_total Finsupp.apply_totalₓ'. -/
theorem apply_total (f : M →ₗ[R] M') (v) (l : α →₀ R) :
f (Finsupp.total α M R v l) = Finsupp.total α M' R (f ∘ v) l := by
@@ -932,9 +932,9 @@ theorem apply_total (f : M →ₗ[R] M') (v) (l : α →₀ R) :
/- warning: finsupp.total_unique -> Finsupp.total_unique is a dubious translation:
lean 3 declaration is
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but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] [_inst_11 : Unique.{succ u3} α] (l : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (v : α -> M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 v) l) (HSMul.hSMul.{u2, u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M M (instHSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M (SMulZeroClass.toSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M _inst_1 _inst_3 _inst_4))))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) α (fun (_x : α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) _x) (Finsupp.funLike.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) l (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) (v (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))))
+ forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] [_inst_11 : Unique.{succ u3} α] (l : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (v : α -> M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 v) l) (HSMul.hSMul.{u2, u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M M (instHSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M (SMulZeroClass.toSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) M _inst_1 _inst_3 _inst_4))))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) α (fun (_x : α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => R) _x) (Finsupp.funLike.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) l (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))) (v (Inhabited.default.{succ u3} α (Unique.instInhabited.{succ u3} α _inst_11))))
Case conversion may be inaccurate. Consider using '#align finsupp.total_unique Finsupp.total_uniqueₓ'. -/
theorem total_unique [Unique α] (l : α →₀ R) (v) :
Finsupp.total α M R v l = l default • v default := by rw [← total_single, ← unique_single l]
@@ -944,7 +944,7 @@ theorem total_unique [Unique α] (l : α →₀ R) (v) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {v : α -> M}, (Function.Surjective.{succ u1, succ u2} α M v) -> (Function.Surjective.{max (succ u1) (succ u3), succ u2} (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {v : α -> M}, (Function.Surjective.{succ u3, succ u2} α M v) -> (Function.Surjective.{max (succ u3) (succ u1), succ u2} (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u1), succ u2} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 v)))
+ forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {v : α -> M}, (Function.Surjective.{succ u3, succ u2} α M v) -> (Function.Surjective.{max (succ u3) (succ u1), succ u2} (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u1), succ u2} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 v)))
Case conversion may be inaccurate. Consider using '#align finsupp.total_surjective Finsupp.total_surjectiveₓ'. -/
theorem total_surjective (h : Function.Surjective v) :
Function.Surjective (Finsupp.total α M R v) :=
@@ -958,7 +958,7 @@ theorem total_surjective (h : Function.Surjective v) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {v : α -> M}, (Function.Surjective.{succ u1, succ u2} α M v) -> (Eq.{succ u2} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) (LinearMap.range.{u3, u3, max u1 u3, u2, max (max u1 u3) u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.semilinearMapClass.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R _inst_1) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v)) (Top.top.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasTop.{u3, u2} R M _inst_1 _inst_3 _inst_4)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {v : α -> M}, (Function.Surjective.{succ u3, succ u2} α M v) -> (Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (LinearMap.range.{u1, u1, max u3 u1, u2, max (max u3 u2) u1} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 v)) (Top.top.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instTopSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)))
+ forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {v : α -> M}, (Function.Surjective.{succ u3, succ u2} α M v) -> (Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (LinearMap.range.{u1, u1, max u3 u1, u2, max (max u3 u2) u1} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 v)) (Top.top.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instTopSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)))
Case conversion may be inaccurate. Consider using '#align finsupp.total_range Finsupp.total_rangeₓ'. -/
theorem total_range (h : Function.Surjective v) : (Finsupp.total α M R v).range = ⊤ :=
range_eq_top.2 <| total_surjective R h
@@ -968,7 +968,7 @@ theorem total_range (h : Function.Surjective v) : (Finsupp.total α M R v).range
lean 3 declaration is
forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] (M : Type.{u2}) [_inst_11 : AddCommMonoid.{u2} M] [_inst_12 : Module.{u1, u2} R M _inst_1 _inst_11], Function.Surjective.{max (succ u2) (succ u1), succ u2} (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (coeFn.{max (succ (max u2 u1)) (succ u2), max (succ (max u2 u1)) (succ u2)} (LinearMap.{u1, u1, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_11 (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_12) (fun (_x : LinearMap.{u1, u1, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_11 (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_12) => (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u2} R R (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_11 (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_12 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} M M R _inst_1 _inst_11 _inst_12 (id.{succ u2} M)))
but is expected to have type
- forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] (M : Type.{u2}) [_inst_11 : AddCommMonoid.{u2} M] [_inst_12 : Module.{u1, u2} R M _inst_1 _inst_11], Function.Surjective.{max (succ u1) (succ u2), succ u2} (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_11 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_12) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u2} R R (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_11 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_12 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} M M R _inst_1 _inst_11 _inst_12 (id.{succ u2} M)))
+ forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] (M : Type.{u2}) [_inst_11 : AddCommMonoid.{u2} M] [_inst_12 : Module.{u1, u2} R M _inst_1 _inst_11], Function.Surjective.{max (succ u1) (succ u2), succ u2} (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_11 (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_12) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u2} R R (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_11 (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_12 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} M M R _inst_1 _inst_11 _inst_12 (id.{succ u2} M)))
Case conversion may be inaccurate. Consider using '#align finsupp.total_id_surjective Finsupp.total_id_surjectiveₓ'. -/
/-- Any module is a quotient of a free module. This is stated as surjectivity of
`finsupp.total M M R id : (M →₀ R) →ₗ[R] M`. -/
@@ -981,7 +981,7 @@ theorem total_id_surjective (M) [AddCommMonoid M] [Module R M] :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {v : α -> M}, Eq.{succ u2} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) (LinearMap.range.{u3, u3, max u1 u3, u2, max (max u1 u3) u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.semilinearMapClass.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R _inst_1) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v)) (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.range.{u2, succ u1} M α v))
but is expected to have type
- forall {α : Type.{u1}} {M : Type.{u3}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_1 _inst_3] {v : α -> M}, Eq.{succ u3} (Submodule.{u2, u3} R M _inst_1 _inst_3 _inst_4) (LinearMap.range.{u2, u2, max u1 u2, u3, max (max u1 u3) u2} R R (Finsupp.{u1, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, max u2 u1, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, max u1 u2, u3} R R (Finsupp.{u1, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R _inst_1) (Finsupp.total.{u1, u3, u2} α M R _inst_1 _inst_3 _inst_4 v)) (Submodule.span.{u2, u3} R M _inst_1 _inst_3 _inst_4 (Set.range.{u3, succ u1} M α v))
+ forall {α : Type.{u1}} {M : Type.{u3}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_1 _inst_3] {v : α -> M}, Eq.{succ u3} (Submodule.{u2, u3} R M _inst_1 _inst_3 _inst_4) (LinearMap.range.{u2, u2, max u1 u2, u3, max (max u1 u3) u2} R R (Finsupp.{u1, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, max u2 u1, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, max u1 u2, u3} R R (Finsupp.{u1, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R _inst_1) (Finsupp.total.{u1, u3, u2} α M R _inst_1 _inst_3 _inst_4 v)) (Submodule.span.{u2, u3} R M _inst_1 _inst_3 _inst_4 (Set.range.{u3, succ u1} M α v))
Case conversion may be inaccurate. Consider using '#align finsupp.range_total Finsupp.range_totalₓ'. -/
theorem range_total : (Finsupp.total α M R v).range = span R (range v) :=
by
@@ -1005,7 +1005,7 @@ theorem range_total : (Finsupp.total α M R v).range = span R (range v) :=
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {α' : Type.{u4}} {M' : Type.{u5}} [_inst_9 : AddCommMonoid.{u5} M'] [_inst_10 : Module.{u3, u5} R M' _inst_1 _inst_9] {v : α -> M} {v' : α' -> M'} (f : α -> α') (g : LinearMap.{u3, u3, u2, u5} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_3 _inst_9 _inst_4 _inst_10), (forall (i : α), Eq.{succ u5} M' (coeFn.{max (succ u2) (succ u5), max (succ u2) (succ u5)} (LinearMap.{u3, u3, u2, u5} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_3 _inst_9 _inst_4 _inst_10) (fun (_x : LinearMap.{u3, u3, u2, u5} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_3 _inst_9 _inst_4 _inst_10) => M -> M') (LinearMap.hasCoeToFun.{u3, u3, u2, u5} R R M M' _inst_1 _inst_1 _inst_3 _inst_9 _inst_4 _inst_10 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) g (v i)) (v' (f i))) -> (Eq.{max (succ (max u1 u3)) (succ u5)} (LinearMap.{u3, u3, max u1 u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) M' (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_10) (LinearMap.comp.{u3, u3, u3, max u1 u3, max u4 u3, u5} R R R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) (Finsupp.{u4, u3} α' R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M' _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.addCommMonoid.{u4, u3} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Finsupp.module.{u4, u3, u3} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_10 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomCompTriple.right_ids.{u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u4, u5, u3} α' M' R _inst_1 _inst_9 _inst_10 v') (Finsupp.lmapDomain.{u1, u3, u3, u4} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) α' f)) (LinearMap.comp.{u3, u3, u3, max u1 u3, u2, u5} R R R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) M M' _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 _inst_9 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 _inst_10 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomCompTriple.right_ids.{u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) g (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v)))
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u4}} (R : Type.{u5}) {_inst_1 : Type.{u1}} {_inst_3 : Type.{u3}} [_inst_4 : Semiring.{u5} R] [α' : AddCommMonoid.{u3} _inst_3] [M' : AddCommMonoid.{u4} M] [_inst_9 : Module.{u5, u3} R _inst_3 _inst_4 α'] [_inst_10 : Module.{u5, u4} R M _inst_4 M'] {v : α -> M} {v' : _inst_1 -> _inst_3} (f : α -> _inst_1) (g : LinearMap.{u5, u5, u4, u3} R R _inst_4 _inst_4 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) M _inst_3 M' α' _inst_10 _inst_9), (forall (i : α), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => _inst_3) (v i)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_4 _inst_4 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) M _inst_3 M' α' _inst_10 _inst_9) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M _inst_3 _inst_4 _inst_4 M' α' _inst_10 _inst_9 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) g (v i)) (v' (f i))) -> (Eq.{max (max (succ u2) (succ u5)) (succ u3)} (LinearMap.{u5, u5, max u5 u2, u3} R R _inst_4 _inst_4 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (Finsupp.{u2, u5} α R (AddMonoid.toZero.{u5} R (AddCommMonoid.toAddMonoid.{u5} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))))) _inst_3 (Finsupp.addCommMonoid.{u2, u5} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))) α' (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u5, u5} α R R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Semiring.toModule.{u5} R _inst_4)) _inst_9) (LinearMap.comp.{u5, u5, u5, max u5 u2, max u5 u1, u3} R R R (Finsupp.{u2, u5} α R (AddMonoid.toZero.{u5} R (AddCommMonoid.toAddMonoid.{u5} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))))) (Finsupp.{u1, u5} _inst_1 R (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_4))) _inst_3 _inst_4 _inst_4 _inst_4 (Finsupp.addCommMonoid.{u2, u5} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))) (Finsupp.addCommMonoid.{u1, u5} _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))) α' (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u5, u5} α R R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Semiring.toModule.{u5} R _inst_4)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u5, u5} _inst_1 R R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Semiring.toModule.{u5} R _inst_4)) _inst_9 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHomCompTriple.ids.{u5, u5} R R _inst_4 _inst_4 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Finsupp.total.{u1, u3, u5} _inst_1 _inst_3 R _inst_4 α' _inst_9 v') (Finsupp.lmapDomain.{u2, u5, u5, u1} α R R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Semiring.toModule.{u5} R _inst_4) _inst_1 f)) (LinearMap.comp.{u5, u5, u5, max u2 u5, u4, u3} R R R (Finsupp.{u2, u5} α R (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_4))) M _inst_3 _inst_4 _inst_4 _inst_4 (Finsupp.addCommMonoid.{u2, u5} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))) M' α' (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u5, u5} α R R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Semiring.toModule.{u5} R _inst_4)) _inst_10 _inst_9 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHomCompTriple.ids.{u5, u5} R R _inst_4 _inst_4 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) g (Finsupp.total.{u2, u4, u5} α M R _inst_4 M' _inst_10 v)))
+ forall {α : Type.{u2}} {M : Type.{u4}} (R : Type.{u5}) {_inst_1 : Type.{u1}} {_inst_3 : Type.{u3}} [_inst_4 : Semiring.{u5} R] [α' : AddCommMonoid.{u3} _inst_3] [M' : AddCommMonoid.{u4} M] [_inst_9 : Module.{u5, u3} R _inst_3 _inst_4 α'] [_inst_10 : Module.{u5, u4} R M _inst_4 M'] {v : α -> M} {v' : _inst_1 -> _inst_3} (f : α -> _inst_1) (g : LinearMap.{u5, u5, u4, u3} R R _inst_4 _inst_4 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) M _inst_3 M' α' _inst_10 _inst_9), (forall (i : α), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => _inst_3) (v i)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_4 _inst_4 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) M _inst_3 M' α' _inst_10 _inst_9) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M _inst_3 _inst_4 _inst_4 M' α' _inst_10 _inst_9 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) g (v i)) (v' (f i))) -> (Eq.{max (max (succ u2) (succ u5)) (succ u3)} (LinearMap.{u5, u5, max u5 u2, u3} R R _inst_4 _inst_4 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (Finsupp.{u2, u5} α R (AddMonoid.toZero.{u5} R (AddCommMonoid.toAddMonoid.{u5} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))))) _inst_3 (Finsupp.addCommMonoid.{u2, u5} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))) α' (Finsupp.module.{u2, u5, u5} α R R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Semiring.toModule.{u5} R _inst_4)) _inst_9) (LinearMap.comp.{u5, u5, u5, max u5 u2, max u5 u1, u3} R R R (Finsupp.{u2, u5} α R (AddMonoid.toZero.{u5} R (AddCommMonoid.toAddMonoid.{u5} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))))) (Finsupp.{u1, u5} _inst_1 R (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_4))) _inst_3 _inst_4 _inst_4 _inst_4 (Finsupp.addCommMonoid.{u2, u5} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))) (Finsupp.addCommMonoid.{u1, u5} _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))) α' (Finsupp.module.{u2, u5, u5} α R R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Semiring.toModule.{u5} R _inst_4)) (Finsupp.module.{u1, u5, u5} _inst_1 R R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Semiring.toModule.{u5} R _inst_4)) _inst_9 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHomCompTriple.ids.{u5, u5} R R _inst_4 _inst_4 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Finsupp.total.{u1, u3, u5} _inst_1 _inst_3 R _inst_4 α' _inst_9 v') (Finsupp.lmapDomain.{u2, u5, u5, u1} α R R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Semiring.toModule.{u5} R _inst_4) _inst_1 f)) (LinearMap.comp.{u5, u5, u5, max u2 u5, u4, u3} R R R (Finsupp.{u2, u5} α R (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_4))) M _inst_3 _inst_4 _inst_4 _inst_4 (Finsupp.addCommMonoid.{u2, u5} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)))) M' α' (Finsupp.module.{u2, u5, u5} α R R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) (Semiring.toModule.{u5} R _inst_4)) _inst_10 _inst_9 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4)) (RingHomCompTriple.ids.{u5, u5} R R _inst_4 _inst_4 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_4))) g (Finsupp.total.{u2, u4, u5} α M R _inst_4 M' _inst_10 v)))
Case conversion may be inaccurate. Consider using '#align finsupp.lmap_domain_total Finsupp.lmapDomain_totalₓ'. -/
theorem lmapDomain_total (f : α → α') (g : M →ₗ[R] M') (h : ∀ i, g (v i) = v' (f i)) :
(Finsupp.total α' M' R v').comp (lmapDomain R R f) = g.comp (Finsupp.total α M R v) := by
@@ -1016,7 +1016,7 @@ theorem lmapDomain_total (f : α → α') (g : M →ₗ[R] M') (h : ∀ i, g (v
lean 3 declaration is
forall {α : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] {α' : Type.{u3}} {M' : Type.{u4}} [_inst_9 : AddCommMonoid.{u4} M'] [_inst_10 : Module.{u2, u4} R M' _inst_1 _inst_9] {v' : α' -> M'} (f : α -> α'), Eq.{max (succ (max u1 u2)) (succ u4)} (LinearMap.{u2, u2, max u1 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} α R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) M' (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) (LinearMap.comp.{u2, u2, u2, max u1 u2, max u3 u2, u4} R R R (Finsupp.{u1, u2} α R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.right_ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u4, u2} α' M' R _inst_1 _inst_9 _inst_10 v') (Finsupp.lmapDomain.{u1, u2, u2, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1) α' f)) (Finsupp.total.{u1, u4, u2} α M' R _inst_1 _inst_9 _inst_10 (Function.comp.{succ u1, succ u3, succ u4} α α' M' v' f))
but is expected to have type
- forall {α : Type.{u4}} (R : Type.{u3}) {_inst_1 : Type.{u1}} {α' : Type.{u2}} [M' : Semiring.{u3} R] [_inst_9 : AddCommMonoid.{u2} α'] [_inst_10 : Module.{u3, u2} R α' M' _inst_9] {v' : _inst_1 -> α'} (f : α -> _inst_1), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (LinearMap.{u3, u3, max u3 u4, u2} R R M' M' (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')) (Finsupp.{u4, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')))))) α' (Finsupp.addCommMonoid.{u4, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')))) _inst_9 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u3, u3} α R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) (Semiring.toModule.{u3} R M')) _inst_10) (LinearMap.comp.{u3, u3, u3, max u3 u4, max u3 u1, u2} R R R (Finsupp.{u4, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')))))) (Finsupp.{u1, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) α' M' M' M' (Finsupp.addCommMonoid.{u4, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')))) (Finsupp.addCommMonoid.{u1, u3} _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')))) _inst_9 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u3, u3} α R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) (Semiring.toModule.{u3} R M')) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u3} _inst_1 R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) (Semiring.toModule.{u3} R M')) _inst_10 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')) (RingHomCompTriple.ids.{u3, u3} R R M' M' (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) (Finsupp.total.{u1, u2, u3} _inst_1 α' R M' _inst_9 _inst_10 v') (Finsupp.lmapDomain.{u4, u3, u3, u1} α R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) (Semiring.toModule.{u3} R M') _inst_1 f)) (Finsupp.total.{u4, u2, u3} α α' R M' _inst_9 _inst_10 (Function.comp.{succ u4, succ u1, succ u2} α _inst_1 α' v' f))
+ forall {α : Type.{u4}} (R : Type.{u3}) {_inst_1 : Type.{u1}} {α' : Type.{u2}} [M' : Semiring.{u3} R] [_inst_9 : AddCommMonoid.{u2} α'] [_inst_10 : Module.{u3, u2} R α' M' _inst_9] {v' : _inst_1 -> α'} (f : α -> _inst_1), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (LinearMap.{u3, u3, max u3 u4, u2} R R M' M' (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')) (Finsupp.{u4, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')))))) α' (Finsupp.addCommMonoid.{u4, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')))) _inst_9 (Finsupp.module.{u4, u3, u3} α R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) (Semiring.toModule.{u3} R M')) _inst_10) (LinearMap.comp.{u3, u3, u3, max u3 u4, max u3 u1, u2} R R R (Finsupp.{u4, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')))))) (Finsupp.{u1, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) α' M' M' M' (Finsupp.addCommMonoid.{u4, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')))) (Finsupp.addCommMonoid.{u1, u3} _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')))) _inst_9 (Finsupp.module.{u4, u3, u3} α R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) (Semiring.toModule.{u3} R M')) (Finsupp.module.{u1, u3, u3} _inst_1 R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) (Semiring.toModule.{u3} R M')) _inst_10 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')) (RingHomCompTriple.ids.{u3, u3} R R M' M' (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) (Finsupp.total.{u1, u2, u3} _inst_1 α' R M' _inst_9 _inst_10 v') (Finsupp.lmapDomain.{u4, u3, u3, u1} α R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) (Semiring.toModule.{u3} R M') _inst_1 f)) (Finsupp.total.{u4, u2, u3} α α' R M' _inst_9 _inst_10 (Function.comp.{succ u4, succ u1, succ u2} α _inst_1 α' v' f))
Case conversion may be inaccurate. Consider using '#align finsupp.total_comp_lmap_domain Finsupp.total_comp_lmapDomainₓ'. -/
theorem total_comp_lmapDomain (f : α → α') :
(Finsupp.total α' M' R v').comp (Finsupp.lmapDomain R R f) = Finsupp.total α M' R (v' ∘ f) :=
@@ -1029,7 +1029,7 @@ theorem total_comp_lmapDomain (f : α → α') :
lean 3 declaration is
forall {α : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] {α' : Type.{u3}} {M' : Type.{u4}} [_inst_9 : AddCommMonoid.{u4} M'] [_inst_10 : Module.{u2, u4} R M' _inst_1 _inst_9] {v' : α' -> M'} (f : Function.Embedding.{succ u1, succ u3} α α') (l : Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))), Eq.{succ u4} M' (coeFn.{max (succ (max u3 u2)) (succ u4), max (succ (max u3 u2)) (succ u4)} (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) (fun (_x : LinearMap.{u2, u2, max u3 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) => (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M') (LinearMap.hasCoeToFun.{u2, u2, max u3 u2, u4} R R (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u4, u2} α' M' R _inst_1 _inst_9 _inst_10 v') (Finsupp.embDomain.{u1, u3, u2} α α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) f l)) (coeFn.{max (succ (max u1 u2)) (succ u4), max (succ (max u1 u2)) (succ u4)} (LinearMap.{u2, u2, max u1 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) (fun (_x : LinearMap.{u2, u2, max u1 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) => (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M') (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u4} R R (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u1, u4, u2} α M' R _inst_1 _inst_9 _inst_10 (Function.comp.{succ u1, succ u3, succ u4} α α' M' v' (coeFn.{max 1 (succ u1) (succ u3), max (succ u1) (succ u3)} (Function.Embedding.{succ u1, succ u3} α α') (fun (_x : Function.Embedding.{succ u1, succ u3} α α') => α -> α') (Function.Embedding.hasCoeToFun.{succ u1, succ u3} α α') f))) l)
but is expected to have type
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+ forall {α : Type.{u4}} (R : Type.{u2}) {_inst_1 : Type.{u3}} {α' : Type.{u1}} [M' : Semiring.{u2} R] [_inst_9 : AddCommMonoid.{u1} α'] [_inst_10 : Module.{u2, u1} R α' M' _inst_9] {v' : _inst_1 -> α'} (f : Function.Embedding.{succ u4, succ u3} α _inst_1) (l : Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) => α') (Finsupp.embDomain.{u4, u3, u2} α _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M')) f l)) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R M' M' (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')) (Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) α' (Finsupp.addCommMonoid.{u3, u2} _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')))) _inst_9 (Finsupp.module.{u3, u2, u2} _inst_1 R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Semiring.toModule.{u2} R M')) _inst_10) (Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) (fun (_x : Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) => α') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) α' M' M' (Finsupp.addCommMonoid.{u3, u2} _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')))) _inst_9 (Finsupp.module.{u3, u2, u2} _inst_1 R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Semiring.toModule.{u2} R M')) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Finsupp.total.{u3, u1, u2} _inst_1 α' R M' _inst_9 _inst_10 v') (Finsupp.embDomain.{u4, u3, u2} α _inst_1 R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M')) f l)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u1), max (succ u4) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u4, u1} R R M' M' (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) α' (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')))) _inst_9 (Finsupp.module.{u4, u2, u2} α R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Semiring.toModule.{u2} R M')) _inst_10) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) (fun (_x : Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) => α') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u1} R R (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R M'))) α' M' M' (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M')))) _inst_9 (Finsupp.module.{u4, u2, u2} α R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Semiring.toModule.{u2} R M')) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R M'))) (Finsupp.total.{u4, u1, u2} α α' R M' _inst_9 _inst_10 (Function.comp.{succ u4, succ u3, succ u1} α _inst_1 α' v' (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Function.Embedding.{succ u4, succ u3} α _inst_1) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => _inst_1) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u3), succ u4, succ u3} (Function.Embedding.{succ u4, succ u3} α _inst_1) α _inst_1 (Function.instEmbeddingLikeEmbedding.{succ u4, succ u3} α _inst_1)) f))) l)
Case conversion may be inaccurate. Consider using '#align finsupp.total_emb_domain Finsupp.total_embDomainₓ'. -/
@[simp]
theorem total_embDomain (f : α ↪ α') (l : α →₀ R) :
@@ -1041,7 +1041,7 @@ theorem total_embDomain (f : α ↪ α') (l : α →₀ R) :
lean 3 declaration is
forall {α : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] {α' : Type.{u3}} {M' : Type.{u4}} [_inst_9 : AddCommMonoid.{u4} M'] [_inst_10 : Module.{u2, u4} R M' _inst_1 _inst_9] {v' : α' -> M'} (f : α -> α') (l : Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))), Eq.{succ u4} M' (coeFn.{max (succ (max u3 u2)) (succ u4), max (succ (max u3 u2)) (succ u4)} (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) (fun (_x : LinearMap.{u2, u2, max u3 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) => (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M') (LinearMap.hasCoeToFun.{u2, u2, max u3 u2, u4} R R (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u4, u2} α' M' R _inst_1 _inst_9 _inst_10 v') (Finsupp.mapDomain.{u1, u3, u2} α α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f l)) (coeFn.{max (succ (max u1 u2)) (succ u4), max (succ (max u1 u2)) (succ u4)} (LinearMap.{u2, u2, max u1 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) (fun (_x : LinearMap.{u2, u2, max u1 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) => (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M') (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u4} R R (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u1, u4, u2} α M' R _inst_1 _inst_9 _inst_10 (Function.comp.{succ u1, succ u3, succ u4} α α' M' v' f)) l)
but is expected to have type
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+ forall {α : Type.{u4}} (R : Type.{u3}) {_inst_1 : Type.{u1}} {α' : Type.{u2}} [M' : Semiring.{u3} R] [_inst_9 : AddCommMonoid.{u2} α'] [_inst_10 : Module.{u3, u2} R α' M' _inst_9] {v' : _inst_1 -> α'} (f : α -> _inst_1) (l : Finsupp.{u4, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u1, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) => α') (Finsupp.mapDomain.{u4, u1, u3} α _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) f l)) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u1), succ u2} (LinearMap.{u3, u3, max u3 u1, u2} R R M' M' (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')) (Finsupp.{u1, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) α' (Finsupp.addCommMonoid.{u1, u3} _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')))) _inst_9 (Finsupp.module.{u1, u3, u3} _inst_1 R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) (Semiring.toModule.{u3} R M')) _inst_10) (Finsupp.{u1, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) (fun (_x : Finsupp.{u1, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u1, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) => α') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u1, u2} R R (Finsupp.{u1, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) α' M' M' (Finsupp.addCommMonoid.{u1, u3} _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')))) _inst_9 (Finsupp.module.{u1, u3, u3} _inst_1 R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) (Semiring.toModule.{u3} R M')) _inst_10 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) (Finsupp.total.{u1, u2, u3} _inst_1 α' R M' _inst_9 _inst_10 v') (Finsupp.mapDomain.{u4, u1, u3} α _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) f l)) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} R R M' M' (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')) (Finsupp.{u4, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) α' (Finsupp.addCommMonoid.{u4, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')))) _inst_9 (Finsupp.module.{u4, u3, u3} α R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) (Semiring.toModule.{u3} R M')) _inst_10) (Finsupp.{u4, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) (fun (_x : Finsupp.{u4, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u4, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) => α') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} R R (Finsupp.{u4, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R M'))) α' M' M' (Finsupp.addCommMonoid.{u4, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M')))) _inst_9 (Finsupp.module.{u4, u3, u3} α R R M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) (Semiring.toModule.{u3} R M')) _inst_10 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R M'))) (Finsupp.total.{u4, u2, u3} α α' R M' _inst_9 _inst_10 (Function.comp.{succ u4, succ u1, succ u2} α _inst_1 α' v' f)) l)
Case conversion may be inaccurate. Consider using '#align finsupp.total_map_domain Finsupp.total_mapDomainₓ'. -/
@[simp]
theorem total_mapDomain (f : α → α') (l : α →₀ R) :
@@ -1053,7 +1053,7 @@ theorem total_mapDomain (f : α → α') (l : α →₀ R) :
lean 3 declaration is
forall {α : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] {α' : Type.{u3}} {M' : Type.{u4}} [_inst_9 : AddCommMonoid.{u4} M'] [_inst_10 : Module.{u2, u4} R M' _inst_1 _inst_9] {v' : α' -> M'} (f : Equiv.{succ u1, succ u3} α α') (l : Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))), Eq.{succ u4} M' (coeFn.{max (succ (max u3 u2)) (succ u4), max (succ (max u3 u2)) (succ u4)} (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) (fun (_x : LinearMap.{u2, u2, max u3 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) => (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M') (LinearMap.hasCoeToFun.{u2, u2, max u3 u2, u4} R R (Finsupp.{u3, u2} α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u3, u2, u2} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u4, u2} α' M' R _inst_1 _inst_9 _inst_10 v') (Finsupp.equivMapDomain.{u1, u3, u2} α α' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) f l)) (coeFn.{max (succ (max u1 u2)) (succ u4), max (succ (max u1 u2)) (succ u4)} (LinearMap.{u2, u2, max u1 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) (fun (_x : LinearMap.{u2, u2, max u1 u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10) => (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M') (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u4} R R (Finsupp.{u1, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M' _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_9 (Finsupp.module.{u1, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_10 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u1, u4, u2} α M' R _inst_1 _inst_9 _inst_10 (Function.comp.{succ u1, succ u3, succ u4} α α' M' v' (coeFn.{max 1 (max (succ u1) (succ u3)) (succ u3) (succ u1), max (succ u1) (succ u3)} (Equiv.{succ u1, succ u3} α α') (fun (_x : Equiv.{succ u1, succ u3} α α') => α -> α') (Equiv.hasCoeToFun.{succ u1, succ u3} α α') f))) l)
but is expected to have type
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Case conversion may be inaccurate. Consider using '#align finsupp.total_equiv_map_domain Finsupp.total_equivMapDomainₓ'. -/
@[simp]
theorem total_equivMapDomain (f : α ≃ α') (l : α →₀ R) :
@@ -1065,7 +1065,7 @@ theorem total_equivMapDomain (f : α ≃ α') (l : α →₀ R) :
lean 3 declaration is
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Case conversion may be inaccurate. Consider using '#align finsupp.span_eq_range_total Finsupp.span_eq_range_totalₓ'. -/
/-- A version of `finsupp.range_total` which is useful for going in the other direction -/
theorem span_eq_range_total (s : Set M) : span R s = (Finsupp.total s M R coe).range := by
@@ -1076,7 +1076,7 @@ theorem span_eq_range_total (s : Set M) : span R s = (Finsupp.total s M R coe).r
lean 3 declaration is
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but is expected to have type
- forall {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u2} M) (x : M), Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 s)) (Exists.{max (succ u2) (succ u1)} (Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (l : Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} (Set.Elem.{u2} M s) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u1, u1} (Set.Elem.{u2} M s) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u2} R R (Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} (Set.Elem.{u2} M s) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u1, u1} (Set.Elem.{u2} M s) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} (Set.Elem.{u2} M s) M R _inst_1 _inst_3 _inst_4 (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s))) l) x))
+ forall {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u2} M) (x : M), Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 s)) (Exists.{max (succ u2) (succ u1)} (Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (l : Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} (Set.Elem.{u2} M s) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u1, u1} (Set.Elem.{u2} M s) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u2} R R (Finsupp.{u2, u1} (Set.Elem.{u2} M s) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} (Set.Elem.{u2} M s) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u1, u1} (Set.Elem.{u2} M s) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} (Set.Elem.{u2} M s) M R _inst_1 _inst_3 _inst_4 (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s))) l) x))
Case conversion may be inaccurate. Consider using '#align finsupp.mem_span_iff_total Finsupp.mem_span_iff_totalₓ'. -/
theorem mem_span_iff_total (s : Set M) (x : M) :
x ∈ span R s ↔ ∃ l : s →₀ R, Finsupp.total s M R coe l = x :=
@@ -1102,7 +1102,7 @@ variable (R)
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {v : α -> M} (s : Set.{u1} α), Eq.{succ u2} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s)) (Submodule.map.{u3, u3, max u1 u3, u2, max (max u1 u3) u2} R R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomSurjective.ids.{u3} R _inst_1) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.semilinearMapClass.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v) (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {v : α -> M} (s : Set.{u3} α), Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)) (Submodule.map.{u1, u1, max u1 u3, u2, max (max u3 u2) u1} R R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 v) (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s))
+ forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {v : α -> M} (s : Set.{u3} α), Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)) (Submodule.map.{u1, u1, max u1 u3, u2, max (max u3 u2) u1} R R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 v) (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s))
Case conversion may be inaccurate. Consider using '#align finsupp.span_image_eq_map_total Finsupp.span_image_eq_map_totalₓ'. -/
theorem span_image_eq_map_total (s : Set α) :
span R (v '' s) = Submodule.map (Finsupp.total α M R v) (supported R R s) :=
@@ -1128,7 +1128,7 @@ theorem span_image_eq_map_total (s : Set α) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {v : α -> M} {s : Set.{u1} α} {x : M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u3, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s))) (Exists.{succ (max u1 u3)} (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (fun (l : Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) => Exists.{0} (Membership.Mem.{max u1 u3, max u1 u3} (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (SetLike.hasMem.{max u1 u3, max u1 u3} (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) (Submodule.setLike.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)))) l (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s)) (fun (H : Membership.Mem.{max u1 u3, max u1 u3} (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (SetLike.hasMem.{max u1 u3, max u1 u3} (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) (Submodule.setLike.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)))) l (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s)) => Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v) l) x)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {v : α -> M} {s : Set.{u3} α} {x : M}, Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (Exists.{succ (max u3 u1)} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (fun (l : Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) => And (Membership.mem.{max u3 u1, max u1 u3} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{max u3 u1, max u3 u1} (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.instSetLikeSubmodule.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) l (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u1), succ u2} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (a : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) a) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 v) l) x)))
+ forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {v : α -> M} {s : Set.{u3} α} {x : M}, Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (Exists.{succ (max u3 u1)} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (fun (l : Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) => And (Membership.mem.{max u3 u1, max u1 u3} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{max u3 u1, max u3 u1} (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.instSetLikeSubmodule.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) l (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u1), succ u2} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (a : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) a) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 v) l) x)))
Case conversion may be inaccurate. Consider using '#align finsupp.mem_span_image_iff_total Finsupp.mem_span_image_iff_totalₓ'. -/
theorem mem_span_image_iff_total {s : Set α} {x : M} :
x ∈ span R (v '' s) ↔ ∃ l ∈ supported R R s, Finsupp.total α M R v l = x :=
@@ -1139,9 +1139,9 @@ theorem mem_span_image_iff_total {s : Set α} {x : M} :
/- warning: finsupp.total_option -> Finsupp.total_option is a dubious translation:
lean 3 declaration is
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(Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} (Option.{u1} α) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} (Option.{u1} α) R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} (Option.{u1} α) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} (Option.{u1} α) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} (Option.{u1} α) M R _inst_1 _inst_3 _inst_4 v) f) (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (Finsupp.{u1, u3} (Option.{u1} α) R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (fun (_x : Finsupp.{u1, u3} (Option.{u1} α) R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) => (Option.{u1} α) -> R) (Finsupp.coeFun.{u1, u3} (Option.{u1} α) R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) f (Option.none.{u1} α)) 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(Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (Function.comp.{succ u1, succ u1, succ u2} α (Option.{u1} α) M v (Option.some.{u1} α))) (Finsupp.some.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) f)))
but is expected to have type
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_inst_3)))) (HSMul.hSMul.{u2, u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Option.{u3} α) => R) (Option.none.{u3} α)) M M (instHSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Option.{u3} α) => R) (Option.none.{u3} α)) M (SMulZeroClass.toSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Option.{u3} α) => R) (Option.none.{u3} α)) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Option.{u3} α) => R) (Option.none.{u3} α)) M (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Option.{u3} α) => R) (Option.none.{u3} α)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Option.{u3} α) => R) (Option.none.{u3} α)) _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : 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_inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 (Function.comp.{succ u3, succ u3, succ u1} α (Option.{u3} α) M v (Option.some.{u3} α))) (Finsupp.some.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) f)))
+ forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (v : (Option.{u3} α) -> M) (f : Finsupp.{u3, u2} (Option.{u3} α) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} (Option.{u3} α) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) f) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} (Option.{u3} α) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} (Option.{u3} α) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} (Option.{u3} α) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} (Option.{u3} α) M R _inst_1 _inst_3 _inst_4 v) f) (HAdd.hAdd.{u1, u1, u1} M ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) (Finsupp.some.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) f)) M (instHAdd.{u1} M (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (HSMul.hSMul.{u2, u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Option.{u3} α) => R) (Option.none.{u3} α)) M M (instHSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Option.{u3} α) => R) (Option.none.{u3} α)) M (SMulZeroClass.toSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Option.{u3} α) => R) (Option.none.{u3} α)) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Option.{u3} α) => R) (Option.none.{u3} α)) M (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Option.{u3} α) => R) (Option.none.{u3} α)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Option.{u3} α) => R) (Option.none.{u3} α)) _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Option.{u3} α) => R) (Option.none.{u3} α)) M (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Option.{u3} α) => R) (Option.none.{u3} α)) _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Option.{u3} α) => R) (Option.none.{u3} α)) M _inst_1 _inst_3 _inst_4))))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} (Option.{u3} α) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Option.{u3} α) (fun (_x : Option.{u3} α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Option.{u3} α) => R) _x) (Finsupp.funLike.{u3, u2} (Option.{u3} α) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) f (Option.none.{u3} α)) (v (Option.none.{u3} α))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 (Function.comp.{succ u3, succ u3, succ u1} α (Option.{u3} α) M v (Option.some.{u3} α))) (Finsupp.some.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) f)))
Case conversion may be inaccurate. Consider using '#align finsupp.total_option Finsupp.total_optionₓ'. -/
theorem total_option (v : Option α → M) (f : Option α →₀ R) :
Finsupp.total (Option α) M R v f =
@@ -1153,7 +1153,7 @@ theorem total_option (v : Option α → M) (f : Option α →₀ R) :
lean 3 declaration is
forall {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {α : Type.{u3}} {β : Type.{u4}} (A : α -> M) (B : β -> (Finsupp.{u3, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (f : Finsupp.{u4, u2} β R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))), Eq.{succ u1} M (coeFn.{max (succ (max u3 u2)) (succ u1), max (succ (max u3 u2)) (succ u1)} (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 A) (coeFn.{max (succ (max u4 u2)) (succ (max u3 u2)), max (succ (max u4 u2)) (succ (max u3 u2))} (LinearMap.{u2, u2, max u4 u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u4, u2} β R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (Finsupp.{u3, u2} α R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (Finsupp.addCommMonoid.{u4, u2} β R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u4, u2, u2} β R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (fun (_x : LinearMap.{u2, u2, max u4 u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u4, u2} β R (MulZeroClass.toHasZero.{u2} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} β M R _inst_1 _inst_3 _inst_4 (fun (b : β) => FunLike.coe.{max (max (succ u1) (succ u2)) (succ u4), max (succ u2) (succ u4), succ u1} (LinearMap.{u2, u2, max u2 u4, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u4, u1} R R (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u4, u1, u2} α M R _inst_1 _inst_3 _inst_4 A) (B b))) f)
Case conversion may be inaccurate. Consider using '#align finsupp.total_total Finsupp.total_totalₓ'. -/
theorem total_total {α β : Type _} (A : α → M) (B : β → α →₀ R) (f : β →₀ R) :
Finsupp.total α M R A (Finsupp.total β (α →₀ R) R B f) =
@@ -1171,7 +1171,7 @@ theorem total_total {α β : Type _} (A : α → M) (B : β → α →₀ R) (f
lean 3 declaration is
forall {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (f : (Fin (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> M), Eq.{max (succ u2) (succ u1)} (LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{0, u2} (Fin (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{0, u2} (Fin (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{0, u2, u2} (Fin (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.total.{0, u1, u2} (Fin (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) M R _inst_1 _inst_3 _inst_4 f) (OfNat.ofNat.{max u2 u1} (LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{0, u2} (Fin (Zero.zero.{0} Nat Nat.hasZero)) R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{0, u2} (Fin (Zero.zero.{0} Nat Nat.hasZero)) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{0, u2, u2} (Fin (Zero.zero.{0} Nat Nat.hasZero)) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) 0 (OfNat.mk.{max u2 u1} (LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{0, u2} (Fin (Zero.zero.{0} Nat Nat.hasZero)) R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{0, u2} (Fin (Zero.zero.{0} Nat Nat.hasZero)) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{0, u2, u2} (Fin (Zero.zero.{0} Nat Nat.hasZero)) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) 0 (Zero.zero.{max u2 u1} (LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{0, u2} (Fin (Zero.zero.{0} Nat Nat.hasZero)) R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{0, u2} (Fin (Zero.zero.{0} Nat Nat.hasZero)) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{0, u2, u2} (Fin (Zero.zero.{0} Nat Nat.hasZero)) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.hasZero.{u2, u2, u2, u1} R R (Finsupp.{0, u2} (Fin (Zero.zero.{0} Nat Nat.hasZero)) R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{0, u2} (Fin (Zero.zero.{0} Nat Nat.hasZero)) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{0, u2, u2} (Fin (Zero.zero.{0} Nat Nat.hasZero)) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))
but is expected to have type
- forall {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (f : (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> M), Eq.{max (succ u2) (succ u1)} (LinearMap.{u1, u1, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.total.{0, u2, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) M R _inst_1 _inst_3 _inst_4 f) (OfNat.ofNat.{max u2 u1} (LinearMap.{u1, u1, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) 0 (Zero.toOfNat0.{max u2 u1} (LinearMap.{u1, u1, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (LinearMap.instZeroLinearMap.{u1, u1, u1, u2} R R (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))
+ forall {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (f : (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> M), Eq.{max (succ u2) (succ u1)} (LinearMap.{u1, u1, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.total.{0, u2, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) M R _inst_1 _inst_3 _inst_4 f) (OfNat.ofNat.{max u2 u1} (LinearMap.{u1, u1, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) 0 (Zero.toOfNat0.{max u2 u1} (LinearMap.{u1, u1, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (LinearMap.instZeroLinearMap.{u1, u1, u1, u2} R R (Finsupp.{0, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{0, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{0, u1, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))
Case conversion may be inaccurate. Consider using '#align finsupp.total_fin_zero Finsupp.total_fin_zeroₓ'. -/
@[simp]
theorem total_fin_zero (f : Fin 0 → M) : Finsupp.total (Fin 0) M R f = 0 :=
@@ -1186,7 +1186,7 @@ variable (α) (M) (v)
lean 3 declaration is
forall (α : Type.{u1}) (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (v : α -> M) (s : Set.{u1} α), LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (coeSort.{succ (max u1 u3), succ (succ (max u1 u3))} (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) Type.{max u1 u3} (SetLike.hasCoeToSort.{max u1 u3, max u1 u3} (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) (Submodule.setLike.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)))) (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s)) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u3, u2} R M _inst_1 _inst_3 _inst_4)) (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s))) (Submodule.addCommMonoid.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s)) (Submodule.addCommMonoid.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s))) (Submodule.module.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s)) (Submodule.module.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s)))
but is expected to have type
- forall (α : Type.{u1}) (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (v : α -> M) (s : Set.{u1} α), LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Subtype.{succ (max u1 u3)} (Finsupp.{u1, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (fun (x : Finsupp.{u1, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) => Membership.mem.{max u1 u3, max u1 u3} (Finsupp.{u1, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (Submodule.{u3, max u3 u1} R (Finsupp.{u1, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (SetLike.instMembership.{max u1 u3, max u1 u3} (Submodule.{u3, max u3 u1} R (Finsupp.{u1, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (Finsupp.{u1, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (Submodule.instSetLikeSubmodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)))) x (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u3, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s)))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s)))
+ forall (α : Type.{u1}) (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (v : α -> M) (s : Set.{u1} α), LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Subtype.{succ (max u1 u3)} (Finsupp.{u1, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (fun (x : Finsupp.{u1, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) => Membership.mem.{max u1 u3, max u1 u3} (Finsupp.{u1, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (Submodule.{u3, max u3 u1} R (Finsupp.{u1, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (SetLike.instMembership.{max u1 u3, max u1 u3} (Submodule.{u3, max u3 u1} R (Finsupp.{u1, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (Finsupp.{u1, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (Submodule.instSetLikeSubmodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)))) x (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u3, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s)))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s)))
Case conversion may be inaccurate. Consider using '#align finsupp.total_on Finsupp.totalOnₓ'. -/
/-- `finsupp.total_on M v s` interprets `p : α →₀ R` as a linear combination of a
subset of the vectors in `v`, mapping it to the span of those vectors.
@@ -1204,7 +1204,7 @@ variable {α} {M} {v}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {v : α -> M} (s : Set.{u1} α), Eq.{succ u2} (Submodule.{u3, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u3, u2} R M _inst_1 _inst_3 _inst_4)) (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s))) _inst_1 (Submodule.addCommMonoid.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s))) (Submodule.module.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s)))) (LinearMap.range.{u3, u3, max u1 u3, u2, max (max u1 u3) u2} R R (coeSort.{succ (max u1 u3), succ (succ (max u1 u3))} (Submodule.{u3, max u1 u3} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) (Submodule.setLike.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)))) (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s)) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u3, u2} R M _inst_1 _inst_3 _inst_4)) (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s))) _inst_1 _inst_1 (Submodule.addCommMonoid.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s)) (Submodule.addCommMonoid.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s))) (Submodule.module.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s)) (Submodule.module.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (coeSort.{succ (max u1 u3), succ (succ (max u1 u3))} (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) Type.{max u1 u3} (SetLike.hasCoeToSort.{max u1 u3, max u1 u3} (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) (Submodule.setLike.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)))) (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s)) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u3, u2} R M _inst_1 _inst_3 _inst_4)) (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s))) (Submodule.addCommMonoid.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R 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(Set.image.{u1, u2} α M v s)))) (LinearMap.semilinearMapClass.{u3, u3, max u1 u3, u2} R R (coeSort.{succ (max u1 u3), succ (succ (max u1 u3))} (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) Type.{max u1 u3} (SetLike.hasCoeToSort.{max u1 u3, max u1 u3} (Submodule.{u3, max u1 u3} R (Finsupp.{u1, u3} α R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Finsupp.supported.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) s)) (Submodule.module.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u3, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u1, u2} α M v s))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R _inst_1) (Finsupp.totalOn.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v s)) (Top.top.{u2} (Submodule.{u3, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u3, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u3, u2} R M _inst_1 _inst_3 _inst_4)) 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but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {v : α -> M} (s : Set.{u3} α), Eq.{succ u2} (Submodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))) _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, 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u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.instSetLikeSubmodule.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) x (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, 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(Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Subtype.{succ (max u3 u1)} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (fun (x : Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) => Membership.mem.{max u3 u1, max u3 u1} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{max u3 u1, max u3 u1} (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.instSetLikeSubmodule.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) x (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u3 u1, u2} R R (Subtype.{succ (max u3 u1)} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (fun (x : Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) => Membership.mem.{max u3 u1, max u3 u1} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{max u3 u1, max u3 u1} (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))) _inst_1 _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.totalOn.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 v s)) (Top.top.{u2} (Submodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))) _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))) (Submodule.instTopSubmodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))) _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))))
+ forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {v : α -> M} (s : Set.{u3} α), Eq.{succ u2} (Submodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))) _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))) (LinearMap.range.{u1, u1, max u3 u1, u2, max (max u3 u2) u1} R R (Subtype.{succ (max u3 u1)} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (fun (x : Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) => Membership.mem.{max u3 u1, max u3 u1} (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{max u3 u1, max u3 u1} (Submodule.{u1, max u1 u3} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R 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(Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Finsupp.supported.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (Finsupp.totalOn.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 v s)) (Top.top.{u2} (Submodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))) _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))) (Submodule.instTopSubmodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))) _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Submodule.span.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Set.image.{u3, u2} α M v s)))))
Case conversion may be inaccurate. Consider using '#align finsupp.total_on_range Finsupp.totalOn_rangeₓ'. -/
theorem totalOn_range (s : Set α) : (Finsupp.totalOn α M R v s).range = ⊤ :=
by
@@ -1217,7 +1217,7 @@ theorem totalOn_range (s : Set α) : (Finsupp.totalOn α M R v s).range = ⊤ :=
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {α' : Type.{u4}} {v : α -> M} (f : α' -> α), Eq.{max (succ (max u4 u3)) (succ u2)} (LinearMap.{u3, u3, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u4, u3} α' R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u4, u3} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (Finsupp.total.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4 (Function.comp.{succ u4, succ u1, succ u2} α' α M v f)) (LinearMap.comp.{u3, u3, u3, max u4 u3, max u1 u3, u2} R R R (Finsupp.{u4, u3} α' R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u3} α' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u4, u3, u3} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomCompTriple.right_ids.{u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 v) (Finsupp.lmapDomain.{u4, u3, u3, u1} α' R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1) α f))
but is expected to have type
- forall {α : Type.{u1}} {M : Type.{u4}} (R : Type.{u3}) {_inst_1 : Type.{u2}} [_inst_3 : Semiring.{u3} R] [_inst_4 : AddCommMonoid.{u4} M] [α' : Module.{u3, u4} R M _inst_3 _inst_4] {v : α -> M} (f : _inst_1 -> α), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (LinearMap.{u3, u3, max u3 u2, u4} R R _inst_3 _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3)) (Finsupp.{u2, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) M (Finsupp.addCommMonoid.{u2, u3} _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3)))) _inst_4 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u3} _inst_1 R R _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3))) (Semiring.toModule.{u3} R _inst_3)) α') (Finsupp.total.{u2, u4, u3} _inst_1 M R _inst_3 _inst_4 α' (Function.comp.{succ u2, succ u1, succ u4} _inst_1 α M v f)) (LinearMap.comp.{u3, u3, u3, max u3 u2, max u1 u3, u4} R R R (Finsupp.{u2, u3} _inst_1 R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3)))))) (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) M _inst_3 _inst_3 _inst_3 (Finsupp.addCommMonoid.{u2, u3} _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3)))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3)))) _inst_4 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u3} _inst_1 R R _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3))) (Semiring.toModule.{u3} R _inst_3)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u3} α R R _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3))) (Semiring.toModule.{u3} R _inst_3)) α' (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3)) (RingHomCompTriple.ids.{u3, u3} R R _inst_3 _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3))) (Finsupp.total.{u1, u4, u3} α M R _inst_3 _inst_4 α' v) (Finsupp.lmapDomain.{u2, u3, u3, u1} _inst_1 R R _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3))) (Semiring.toModule.{u3} R _inst_3) α f))
+ forall {α : Type.{u1}} {M : Type.{u4}} (R : Type.{u3}) {_inst_1 : Type.{u2}} [_inst_3 : Semiring.{u3} R] [_inst_4 : AddCommMonoid.{u4} M] [α' : Module.{u3, u4} R M _inst_3 _inst_4] {v : α -> M} (f : _inst_1 -> α), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (LinearMap.{u3, u3, max u3 u2, u4} R R _inst_3 _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3)) (Finsupp.{u2, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) M (Finsupp.addCommMonoid.{u2, u3} _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3)))) _inst_4 (Finsupp.module.{u2, u3, u3} _inst_1 R R _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3))) (Semiring.toModule.{u3} R _inst_3)) α') (Finsupp.total.{u2, u4, u3} _inst_1 M R _inst_3 _inst_4 α' (Function.comp.{succ u2, succ u1, succ u4} _inst_1 α M v f)) (LinearMap.comp.{u3, u3, u3, max u3 u2, max u1 u3, u4} R R R (Finsupp.{u2, u3} _inst_1 R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3)))))) (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) M _inst_3 _inst_3 _inst_3 (Finsupp.addCommMonoid.{u2, u3} _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3)))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3)))) _inst_4 (Finsupp.module.{u2, u3, u3} _inst_1 R R _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3))) (Semiring.toModule.{u3} R _inst_3)) (Finsupp.module.{u1, u3, u3} α R R _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3))) (Semiring.toModule.{u3} R _inst_3)) α' (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3)) (RingHomCompTriple.ids.{u3, u3} R R _inst_3 _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3))) (Finsupp.total.{u1, u4, u3} α M R _inst_3 _inst_4 α' v) (Finsupp.lmapDomain.{u2, u3, u3, u1} _inst_1 R R _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3))) (Semiring.toModule.{u3} R _inst_3) α f))
Case conversion may be inaccurate. Consider using '#align finsupp.total_comp Finsupp.total_compₓ'. -/
theorem total_comp (f : α' → α) :
Finsupp.total α' M R (v ∘ f) = (Finsupp.total α M R v).comp (lmapDomain R R f) :=
@@ -1228,9 +1228,9 @@ theorem total_comp (f : α' → α) :
/- warning: finsupp.total_comap_domain -> Finsupp.total_comapDomain is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {α' : Type.{u4}} {v : α -> M} (f : α -> α') (l : Finsupp.{u4, u3} α' R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (hf : Set.InjOn.{u1, u4} α α' f (Set.preimage.{u1, u4} α α' f ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} α') (Set.{u4} α') (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} α') (Set.{u4} α') (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} α') (Set.{u4} α') (Finset.Set.hasCoeT.{u4} α'))) (Finsupp.support.{u4, u3} α' R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) l)))), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R 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+ forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {α' : Type.{u4}} {v : α -> M} (f : α -> α') (l : Finsupp.{u4, u3} α' R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (hf : Set.InjOn.{u1, u4} α α' f (Set.preimage.{u1, u4} α α' f ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} α') (Set.{u4} α') (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} α') (Set.{u4} α') (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} α') (Set.{u4} α') (Finset.Set.hasCoeT.{u4} α'))) (Finsupp.support.{u4, u3} α' R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) l)))), Eq.{succ u2} M 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but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u1}} (R : Type.{u3}) {_inst_1 : Type.{u4}} [_inst_3 : Semiring.{u3} R] [_inst_4 : AddCommMonoid.{u1} M] [α' : Module.{u3, u1} R M _inst_3 _inst_4] {v : α -> M} (f : α -> _inst_1) (l : Finsupp.{u4, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) (hf : Set.InjOn.{u2, u4} α _inst_1 f (Set.preimage.{u2, u4} α _inst_1 f (Finset.toSet.{u4} _inst_1 (Finsupp.support.{u4, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3)) l)))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) => M) (Finsupp.comapDomain.{u2, u4, u3} α _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3)) f l hf)) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_3 _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3)) (Finsupp.{u2, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) M (Finsupp.addCommMonoid.{u2, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3)))) _inst_4 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u3} α R R _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3))) (Semiring.toModule.{u3} R _inst_3)) α') (Finsupp.{u2, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) (fun (_x : Finsupp.{u2, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) => M) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u1} R R (Finsupp.{u2, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) M _inst_3 _inst_3 (Finsupp.addCommMonoid.{u2, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3)))) _inst_4 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u3} α R R _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3))) (Semiring.toModule.{u3} R _inst_3)) α' (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3))) (Finsupp.total.{u2, u1, u3} α M R _inst_3 _inst_4 α' v) (Finsupp.comapDomain.{u2, u4, u3} α _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3)) f l hf)) (Finset.sum.{u1, u2} M α _inst_4 (Finset.preimage.{u2, u4} α _inst_1 (Finsupp.support.{u4, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3)) l) f hf) (fun (i : α) => HSMul.hSMul.{u3, u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) M M (instHSMul.{u3, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) M (SMulZeroClass.toSMul.{u3, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u3, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) M (MonoidWithZero.toZero.{u3} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) _inst_3)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u3, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) M (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) _inst_3) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (Module.toMulActionWithZero.{u3, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) M _inst_3 _inst_4 α'))))) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Finsupp.{u4, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) _inst_1 (fun (_x : _inst_1) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) _x) (Finsupp.funLike.{u4, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) l (f i)) (v i)))
+ forall {α : Type.{u2}} {M : Type.{u1}} (R : Type.{u3}) {_inst_1 : Type.{u4}} [_inst_3 : Semiring.{u3} R] [_inst_4 : AddCommMonoid.{u1} M] [α' : Module.{u3, u1} R M _inst_3 _inst_4] {v : α -> M} (f : α -> _inst_1) (l : Finsupp.{u4, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) (hf : Set.InjOn.{u2, u4} α _inst_1 f (Set.preimage.{u2, u4} α _inst_1 f (Finset.toSet.{u4} _inst_1 (Finsupp.support.{u4, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3)) l)))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) => M) (Finsupp.comapDomain.{u2, u4, u3} α _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3)) f l hf)) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_3 _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3)) (Finsupp.{u2, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) M (Finsupp.addCommMonoid.{u2, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3)))) _inst_4 (Finsupp.module.{u2, u3, u3} α R R _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3))) (Semiring.toModule.{u3} R _inst_3)) α') (Finsupp.{u2, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) (fun (_x : Finsupp.{u2, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) => M) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u1} R R (Finsupp.{u2, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) M _inst_3 _inst_3 (Finsupp.addCommMonoid.{u2, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3)))) _inst_4 (Finsupp.module.{u2, u3, u3} α R R _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3))) (Semiring.toModule.{u3} R _inst_3)) α' (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_3))) (Finsupp.total.{u2, u1, u3} α M R _inst_3 _inst_4 α' v) (Finsupp.comapDomain.{u2, u4, u3} α _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3)) f l hf)) (Finset.sum.{u1, u2} M α _inst_4 (Finset.preimage.{u2, u4} α _inst_1 (Finsupp.support.{u4, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3)) l) f hf) (fun (i : α) => HSMul.hSMul.{u3, u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) M M (instHSMul.{u3, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) M (SMulZeroClass.toSMul.{u3, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u3, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) M (MonoidWithZero.toZero.{u3} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) _inst_3)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u3, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) M (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) _inst_3) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (Module.toMulActionWithZero.{u3, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) (f i)) M _inst_3 _inst_4 α'))))) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Finsupp.{u4, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) _inst_1 (fun (_x : _inst_1) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : _inst_1) => R) _x) (Finsupp.funLike.{u4, u3} _inst_1 R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_3))) l (f i)) (v i)))
Case conversion may be inaccurate. Consider using '#align finsupp.total_comap_domain Finsupp.total_comapDomainₓ'. -/
theorem total_comapDomain (f : α → α') (l : α' →₀ R) (hf : Set.InjOn f (f ⁻¹' ↑l.support)) :
Finsupp.total α M R v (Finsupp.comapDomain f l hf) =
@@ -1242,7 +1242,7 @@ theorem total_comapDomain (f : α → α') (l : α' →₀ R) (hf : Set.InjOn f
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {s : Finset.{u1} α} {f : α -> R} (g : α -> M) (hf : forall (a : α), (Ne.{succ u3} R (f a) (OfNat.ofNat.{u3} R 0 (OfNat.mk.{u3} R 0 (Zero.zero.{u3} R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))))) -> (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s)), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 g) (Finsupp.onFinset.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) s f hf)) (Finset.sum.{u2, u1} M α _inst_3 s (fun (x : α) => SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) (f x) (g x)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {s : Finset.{u3} α} {f : α -> R} (g : α -> M) (hf : forall (a : α), (Ne.{succ u2} R (f a) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))))) -> (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) (Finsupp.onFinset.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) s f hf)) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 g) (Finsupp.onFinset.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) s f hf)) (Finset.sum.{u1, u3} M α _inst_3 s (fun (x : α) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4))))) (f x) (g x)))
+ forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {s : Finset.{u3} α} {f : α -> R} (g : α -> M) (hf : forall (a : α), (Ne.{succ u2} R (f a) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))))) -> (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) (Finsupp.onFinset.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) s f hf)) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 g) (Finsupp.onFinset.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) s f hf)) (Finset.sum.{u1, u3} M α _inst_3 s (fun (x : α) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4))))) (f x) (g x)))
Case conversion may be inaccurate. Consider using '#align finsupp.total_on_finset Finsupp.total_onFinsetₓ'. -/
theorem total_onFinset {s : Finset α} {f : α → R} (g : α → M) (hf : ∀ a, f a ≠ 0 → a ∈ s) :
Finsupp.total α M R g (Finsupp.onFinset s f hf) = Finset.sum s fun x : α => f x • g x :=
@@ -1260,7 +1260,7 @@ end Total
lean 3 declaration is
forall {M : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {α₁ : Type.{u3}} {α₂ : Type.{u4}}, (Equiv.{succ u3, succ u4} α₁ α₂) -> (LinearEquiv.{u2, u2, max u3 u1, max u4 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (Finsupp.{u3, u1} α₁ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.addCommMonoid.{u3, u1} α₁ M _inst_3) (Finsupp.addCommMonoid.{u4, u1} α₂ M _inst_3) (Finsupp.module.{u3, u1, u2} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u1, u2} α₂ M R _inst_1 _inst_3 _inst_4))
but is expected to have type
- forall {M : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {α₁ : Type.{u3}} {α₂ : Type.{u4}}, (Equiv.{succ u3, succ u4} α₁ α₂) -> (LinearEquiv.{u2, u2, max u1 u3, max u1 u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (Finsupp.{u3, u1} α₁ M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Finsupp.{u4, u1} α₂ M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Finsupp.addCommMonoid.{u3, u1} α₁ M _inst_3) (Finsupp.addCommMonoid.{u4, u1} α₂ M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u2} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u1, u2} α₂ M R _inst_1 _inst_3 _inst_4))
+ forall {M : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {α₁ : Type.{u3}} {α₂ : Type.{u4}}, (Equiv.{succ u3, succ u4} α₁ α₂) -> (LinearEquiv.{u2, u2, max u1 u3, max u1 u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (Finsupp.{u3, u1} α₁ M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Finsupp.{u4, u1} α₂ M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Finsupp.addCommMonoid.{u3, u1} α₁ M _inst_3) (Finsupp.addCommMonoid.{u4, u1} α₂ M _inst_3) (Finsupp.module.{u3, u1, u2} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u1, u2} α₂ M R _inst_1 _inst_3 _inst_4))
Case conversion may be inaccurate. Consider using '#align finsupp.dom_lcongr Finsupp.domLCongrₓ'. -/
/-- An equivalence of domains induces a linear equivalence of finitely supported functions.
@@ -1273,9 +1273,9 @@ protected def domLCongr {α₁ α₂ : Type _} (e : α₁ ≃ α₂) : (α₁
/- warning: finsupp.dom_lcongr_apply -> Finsupp.domLCongr_apply is a dubious translation:
lean 3 declaration is
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but is expected to have type
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_inst_3))))))) (Finsupp.domCongr.{u4, u3, u2} α₁ α₂ M _inst_3 e) v)
+ forall {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {α₁ : Type.{u4}} {α₂ : Type.{u3}} (e : Equiv.{succ u4, succ u3} α₁ α₂) (v : Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))), Eq.{max (succ u2) (succ u3)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) v) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u2), max (succ u3) (succ u2)} (LinearEquiv.{u1, u1, max u2 u4, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{u4, u2} α₁ M 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u2} α₁ M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.add.{u3, u2} α₂ M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (AddMonoid.toAddZeroClass.{max u4 u2} (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addMonoid.{u4, u2} α₁ M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addMonoid.{u3, u2} α₂ M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (AddEquiv.instAddEquivClassAddEquiv.{max u4 u2, max u3 u2} (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.add.{u4, u2} α₁ M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.add.{u3, u2} α₂ M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))))))) (Finsupp.domCongr.{u4, u3, u2} α₁ α₂ M _inst_3 e) v)
Case conversion may be inaccurate. Consider using '#align finsupp.dom_lcongr_apply Finsupp.domLCongr_applyₓ'. -/
@[simp]
theorem domLCongr_apply {α₁ : Type _} {α₂ : Type _} (e : α₁ ≃ α₂) (v : α₁ →₀ M) :
@@ -1287,7 +1287,7 @@ theorem domLCongr_apply {α₁ : Type _} {α₂ : Type _} (e : α₁ ≃ α₂)
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], Eq.{succ (max u1 u2)} (LinearEquiv.{u3, u3, max u1 u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.domLCongr.{u2, u3, u1, u1} M R _inst_1 _inst_3 _inst_4 α α (Equiv.refl.{succ u1} α)) (LinearEquiv.refl.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Eq.{max (succ u3) (succ u2)} (LinearEquiv.{u1, u1, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.domLCongr.{u2, u1, u3, u3} M R _inst_1 _inst_3 _inst_4 α α (Equiv.refl.{succ u3} α)) (LinearEquiv.refl.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Eq.{max (succ u3) (succ u2)} (LinearEquiv.{u1, u1, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.domLCongr.{u2, u1, u3, u3} M R _inst_1 _inst_3 _inst_4 α α (Equiv.refl.{succ u3} α)) (LinearEquiv.refl.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))
Case conversion may be inaccurate. Consider using '#align finsupp.dom_lcongr_refl Finsupp.domLCongr_reflₓ'. -/
@[simp]
theorem domLCongr_refl : Finsupp.domLCongr (Equiv.refl α) = LinearEquiv.refl R (α →₀ M) :=
@@ -1298,7 +1298,7 @@ theorem domLCongr_refl : Finsupp.domLCongr (Equiv.refl α) = LinearEquiv.refl R
lean 3 declaration is
forall {M : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {α₁ : Type.{u3}} {α₂ : Type.{u4}} {α₃ : Type.{u5}} (f : Equiv.{succ u3, succ u4} α₁ α₂) (f₂ : Equiv.{succ u4, succ u5} α₂ α₃), Eq.{max (succ (max u3 u1)) (succ (max u5 u1))} (LinearEquiv.{u2, u2, max u3 u1, max u5 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (Finsupp.{u3, u1} α₁ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u5, u1} α₃ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.addCommMonoid.{u3, u1} α₁ M _inst_3) (Finsupp.addCommMonoid.{u5, u1} α₃ M _inst_3) (Finsupp.module.{u3, u1, u2} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u5, u1, u2} α₃ M R _inst_1 _inst_3 _inst_4)) (LinearEquiv.trans.{u2, u2, u2, max u3 u1, max u4 u1, max u5 u1} R R R (Finsupp.{u3, u1} α₁ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u5, u1} α₃ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α₁ M _inst_3) (Finsupp.addCommMonoid.{u4, u1} α₂ M _inst_3) (Finsupp.addCommMonoid.{u5, u1} α₃ M _inst_3) (Finsupp.module.{u3, u1, u2} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u1, u2} α₂ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u5, u1, u2} α₃ M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.right_ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (RingHomCompTriple.right_ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (Finsupp.domLCongr.{u1, u2, u3, u4} M R _inst_1 _inst_3 _inst_4 α₁ α₂ f) (Finsupp.domLCongr.{u1, u2, u4, u5} M R _inst_1 _inst_3 _inst_4 α₂ α₃ f₂)) (Finsupp.domLCongr.{u1, u2, u3, u5} M R _inst_1 _inst_3 _inst_4 α₁ α₃ (Equiv.trans.{succ u3, succ u4, succ u5} α₁ α₂ α₃ f f₂))
but is expected to have type
- forall {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {α₁ : Type.{u5}} {α₂ : Type.{u4}} {α₃ : Type.{u3}} (f : Equiv.{succ u5, succ u4} α₁ α₂) (f₂ : Equiv.{succ u4, succ u3} α₂ α₃), Eq.{max (max (succ u2) (succ u5)) (succ u3)} (LinearEquiv.{u1, u1, max u5 u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{u5, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₃ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u5, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₃ M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u5, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α₃ M R _inst_1 _inst_3 _inst_4)) (LinearEquiv.trans.{u1, u1, u1, max u5 u2, max u4 u2, max u3 u2} R R R (Finsupp.{u5, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₃ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u5, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α₂ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₃ M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u5, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α₃ M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomCompTriple.ids.{u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomCompTriple.ids.{u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.domLCongr.{u2, u1, u5, u4} M R _inst_1 _inst_3 _inst_4 α₁ α₂ f) (Finsupp.domLCongr.{u2, u1, u4, u3} M R _inst_1 _inst_3 _inst_4 α₂ α₃ f₂)) (Finsupp.domLCongr.{u2, u1, u5, u3} M R _inst_1 _inst_3 _inst_4 α₁ α₃ (Equiv.trans.{succ u5, succ u4, succ u3} α₁ α₂ α₃ f f₂))
+ forall {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {α₁ : Type.{u5}} {α₂ : Type.{u4}} {α₃ : Type.{u3}} (f : Equiv.{succ u5, succ u4} α₁ α₂) (f₂ : Equiv.{succ u4, succ u3} α₂ α₃), Eq.{max (max (succ u2) (succ u5)) (succ u3)} (LinearEquiv.{u1, u1, max u5 u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{u5, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₃ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u5, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₃ M _inst_3) (Finsupp.module.{u5, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α₃ M R _inst_1 _inst_3 _inst_4)) (LinearEquiv.trans.{u1, u1, u1, max u5 u2, max u4 u2, max u3 u2} R R R (Finsupp.{u5, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₃ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u5, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α₂ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₃ M _inst_3) (Finsupp.module.{u5, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α₃ M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomCompTriple.ids.{u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomCompTriple.ids.{u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.domLCongr.{u2, u1, u5, u4} M R _inst_1 _inst_3 _inst_4 α₁ α₂ f) (Finsupp.domLCongr.{u2, u1, u4, u3} M R _inst_1 _inst_3 _inst_4 α₂ α₃ f₂)) (Finsupp.domLCongr.{u2, u1, u5, u3} M R _inst_1 _inst_3 _inst_4 α₁ α₃ (Equiv.trans.{succ u5, succ u4, succ u3} α₁ α₂ α₃ f f₂))
Case conversion may be inaccurate. Consider using '#align finsupp.dom_lcongr_trans Finsupp.domLCongr_transₓ'. -/
theorem domLCongr_trans {α₁ α₂ α₃ : Type _} (f : α₁ ≃ α₂) (f₂ : α₂ ≃ α₃) :
(Finsupp.domLCongr f).trans (Finsupp.domLCongr f₂) =
@@ -1310,7 +1310,7 @@ theorem domLCongr_trans {α₁ α₂ α₃ : Type _} (f : α₁ ≃ α₂) (f₂
lean 3 declaration is
forall {M : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {α₁ : Type.{u3}} {α₂ : Type.{u4}} (f : Equiv.{succ u3, succ u4} α₁ α₂), Eq.{max (succ (max u4 u1)) (succ (max u3 u1))} (LinearEquiv.{u2, u2, max u4 u1, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (Finsupp.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u3, u1} α₁ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.addCommMonoid.{u4, u1} α₂ M _inst_3) (Finsupp.addCommMonoid.{u3, u1} α₁ M _inst_3) (Finsupp.module.{u4, u1, u2} α₂ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u1, u2} α₁ M R _inst_1 _inst_3 _inst_4)) (LinearEquiv.symm.{u2, u2, max u3 u1, max u4 u1} R R (Finsupp.{u3, u1} α₁ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α₁ M _inst_3) (Finsupp.addCommMonoid.{u4, u1} α₂ M _inst_3) (Finsupp.module.{u3, u1, u2} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u1, u2} α₂ M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (Finsupp.domLCongr.{u1, u2, u3, u4} M R _inst_1 _inst_3 _inst_4 α₁ α₂ f)) (Finsupp.domLCongr.{u1, u2, u4, u3} M R _inst_1 _inst_3 _inst_4 α₂ α₁ (Equiv.symm.{succ u3, succ u4} α₁ α₂ f))
but is expected to have type
- forall {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {α₁ : Type.{u4}} {α₂ : Type.{u3}} (f : Equiv.{succ u4, succ u3} α₁ α₂), Eq.{max (max (succ u2) (succ u4)) (succ u3)} (LinearEquiv.{u1, u1, max u3 u2, max u4 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4)) (LinearEquiv.symm.{u1, u1, max u4 u2, max u3 u2} R R (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.domLCongr.{u2, u1, u4, u3} M R _inst_1 _inst_3 _inst_4 α₁ α₂ f)) (Finsupp.domLCongr.{u2, u1, u3, u4} M R _inst_1 _inst_3 _inst_4 α₂ α₁ (Equiv.symm.{succ u4, succ u3} α₁ α₂ f))
+ forall {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {α₁ : Type.{u4}} {α₂ : Type.{u3}} (f : Equiv.{succ u4, succ u3} α₁ α₂), Eq.{max (max (succ u2) (succ u4)) (succ u3)} (LinearEquiv.{u1, u1, max u3 u2, max u4 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4)) (LinearEquiv.symm.{u1, u1, max u4 u2, max u3 u2} R R (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.domLCongr.{u2, u1, u4, u3} M R _inst_1 _inst_3 _inst_4 α₁ α₂ f)) (Finsupp.domLCongr.{u2, u1, u3, u4} M R _inst_1 _inst_3 _inst_4 α₂ α₁ (Equiv.symm.{succ u4, succ u3} α₁ α₂ f))
Case conversion may be inaccurate. Consider using '#align finsupp.dom_lcongr_symm Finsupp.domLCongr_symmₓ'. -/
@[simp]
theorem domLCongr_symm {α₁ α₂ : Type _} (f : α₁ ≃ α₂) :
@@ -1322,7 +1322,7 @@ theorem domLCongr_symm {α₁ α₂ : Type _} (f : α₁ ≃ α₂) :
lean 3 declaration is
forall {M : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {α₁ : Type.{u3}} {α₂ : Type.{u4}} (e : Equiv.{succ u3, succ u4} α₁ α₂) (i : α₁) (m : M), Eq.{max (succ u4) (succ u1)} (Finsupp.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (coeFn.{max (succ (max u3 u1)) (succ (max u4 u1)), max (succ (max u3 u1)) (succ (max u4 u1))} (LinearEquiv.{u2, u2, max u3 u1, max u4 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (Finsupp.{u3, u1} α₁ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.addCommMonoid.{u3, u1} α₁ M _inst_3) (Finsupp.addCommMonoid.{u4, u1} α₂ M _inst_3) (Finsupp.module.{u3, u1, u2} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u1, u2} α₂ M R _inst_1 _inst_3 _inst_4)) (fun (_x : LinearEquiv.{u2, u2, max u3 u1, max u4 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (Finsupp.{u3, u1} α₁ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.addCommMonoid.{u3, u1} α₁ M _inst_3) (Finsupp.addCommMonoid.{u4, u1} α₂ M _inst_3) (Finsupp.module.{u3, u1, u2} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u1, u2} α₂ M R _inst_1 _inst_3 _inst_4)) => (Finsupp.{u3, u1} α₁ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) -> (Finsupp.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (LinearEquiv.hasCoeToFun.{u2, u2, max u3 u1, max u4 u1} R R (Finsupp.{u3, u1} α₁ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α₁ M _inst_3) (Finsupp.addCommMonoid.{u4, u1} α₂ M _inst_3) (Finsupp.module.{u3, u1, u2} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u1, u2} α₂ M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1)) (Finsupp.domLCongr.{u1, u2, u3, u4} M R _inst_1 _inst_3 _inst_4 α₁ α₂ e) (Finsupp.single.{u3, u1} α₁ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) i m)) (Finsupp.single.{u4, u1} α₂ M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (coeFn.{max 1 (max (succ u3) (succ u4)) (succ u4) (succ u3), max (succ u3) (succ u4)} (Equiv.{succ u3, succ u4} α₁ α₂) (fun (_x : Equiv.{succ u3, succ u4} α₁ α₂) => α₁ -> α₂) (Equiv.hasCoeToFun.{succ u3, succ u4} α₁ α₂) e i) m)
but is expected to have type
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(RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4)) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u4 u2, max u3 u2} R R (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1)))))) (Finsupp.domLCongr.{u2, u1, u4, u3} M R _inst_1 _inst_3 _inst_4 α₁ α₂ e) (Finsupp.single.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) i m)) (Finsupp.single.{u3, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α₁) => α₂) i) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Equiv.{succ u4, succ u3} α₁ α₂) α₁ (fun (_x : α₁) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α₁) => α₂) _x) (Equiv.instFunLikeEquiv.{succ u4, succ u3} α₁ α₂) e i) m)
+ forall {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {α₁ : Type.{u4}} {α₂ : Type.{u3}} (e : Equiv.{succ u4, succ u3} α₁ α₂) (i : α₁) (m : M), Eq.{max (succ u2) (succ u3)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.single.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) i m)) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u2), max (succ u3) (succ u2)} (LinearEquiv.{u1, u1, max u2 u4, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (_x : Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _x) (SMulHomClass.toFunLike.{max (max u4 u3) u2, u1, max u4 u2, max u3 u2} (LinearEquiv.{u1, u1, max u2 u4, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4)) R (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulZeroClass.toSMul.{u1, max u4 u2} R (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (AddMonoid.toZero.{max u4 u2} (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (AddCommMonoid.toAddMonoid.{max u4 u2} (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3))) (DistribSMul.toSMulZeroClass.{u1, max u4 u2} R (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (AddMonoid.toAddZeroClass.{max u4 u2} (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (AddCommMonoid.toAddMonoid.{max u4 u2} (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3))) (DistribMulAction.toDistribSMul.{u1, max u4 u2} R (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u4 u2} (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3)) (Module.toDistribMulAction.{u1, max u4 u2} R (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, max u3 u2} R (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3))) (DistribSMul.toSMulZeroClass.{u1, max u3 u2} R (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3))) (DistribMulAction.toDistribSMul.{u1, max u3 u2} R (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3)) (Module.toDistribMulAction.{u1, max u3 u2} R (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u4 u3) u2, u1, max u4 u2, max u3 u2} (LinearEquiv.{u1, u1, max u2 u4, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4)) R (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u4 u2} (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3)) (Module.toDistribMulAction.{u1, max u4 u2} R (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, max u3 u2} R (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4)) (SemilinearMapClass.distribMulActionHomClass.{u1, max u4 u2, max u3 u2, max (max u4 u3) u2} R (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (LinearEquiv.{u1, u1, max u2 u4, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4)) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u4 u2, max u3 u2, max (max u4 u3) u2} R R (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (LinearEquiv.{u1, u1, max u2 u4, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4)) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u4 u2, max u3 u2} R R (Finsupp.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α₂ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u2} α₁ M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α₂ M _inst_3) (Finsupp.module.{u4, u2, u1} α₁ M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α₂ M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1)))))) (Finsupp.domLCongr.{u2, u1, u4, u3} M R _inst_1 _inst_3 _inst_4 α₁ α₂ e) (Finsupp.single.{u4, u2} α₁ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) i m)) (Finsupp.single.{u3, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α₁) => α₂) i) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Equiv.{succ u4, succ u3} α₁ α₂) α₁ (fun (_x : α₁) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α₁) => α₂) _x) (Equiv.instFunLikeEquiv.{succ u4, succ u3} α₁ α₂) e i) m)
Case conversion may be inaccurate. Consider using '#align finsupp.dom_lcongr_single Finsupp.domLCongr_singleₓ'. -/
@[simp]
theorem domLCongr_single {α₁ : Type _} {α₂ : Type _} (e : α₁ ≃ α₂) (i : α₁) (m : M) :
@@ -1334,7 +1334,7 @@ theorem domLCongr_single {α₁ : Type _} {α₂ : Type _} (e : α₁ ≃ α₂)
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {α' : Type.{u4}} (s : Set.{u1} α) (t : Set.{u4} α'), (Equiv.{succ u1, succ u4} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (coeSort.{succ u4, succ (succ u4)} (Set.{u4} α') Type.{u4} (Set.hasCoeToSort.{u4} α') t)) -> (LinearEquiv.{u3, u3, max u1 u2, max u4 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (coeSort.{succ (max u4 u2), succ (succ (max u4 u2))} (Submodule.{u3, max u4 u2} R (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4)) Type.{max u4 u2} (SetLike.hasCoeToSort.{max u4 u2, max u4 u2} (Submodule.{u3, max u4 u2} R (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Submodule.setLike.{u3, max u4 u2} R (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4))) (Finsupp.supported.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4 t)) (Submodule.addCommMonoid.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Submodule.addCommMonoid.{u3, max u4 u2} R (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4 t)) (Submodule.module.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Submodule.module.{u3, max u4 u2} R (Finsupp.{u4, u2} α' M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4 t)))
but is expected to have type
- forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {α' : Type.{u4}} (s : Set.{u1} α) (t : Set.{u4} α'), (Equiv.{succ u1, succ u4} (Set.Elem.{u1} α s) (Set.Elem.{u4} α' t)) -> (LinearEquiv.{u3, u3, max u1 u2, max u2 u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Subtype.{succ (max u1 u2)} (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u1 u2, max u1 u2} (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u3, max u2 u1} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u3, max u2 u1} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) x (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s))) (Subtype.{succ (max u2 u4)} (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u2 u4, max u2 u4} (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u3, max u2 u4} R (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u2 u4, max u2 u4} (Submodule.{u3, max u2 u4} R (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u3, max u2 u4} R (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4))) x (Finsupp.supported.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4 t))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, max u2 u4} R (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4 t)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, max u2 u4} R (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4 t)))
+ forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] {α' : Type.{u4}} (s : Set.{u1} α) (t : Set.{u4} α'), (Equiv.{succ u1, succ u4} (Set.Elem.{u1} α s) (Set.Elem.{u4} α' t)) -> (LinearEquiv.{u3, u3, max u1 u2, max u2 u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Subtype.{succ (max u1 u2)} (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u1 u2, max u1 u2} (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u3, max u2 u1} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u3, max u2 u1} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))) x (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s))) (Subtype.{succ (max u2 u4)} (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (x : Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Membership.mem.{max u2 u4, max u2 u4} (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u3, max u2 u4} R (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u2 u4, max u2 u4} (Submodule.{u3, max u2 u4} R (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u3, max u2 u4} R (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4))) x (Finsupp.supported.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4 t))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, max u2 u4} R (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4 t)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, max u2 u4} R (Finsupp.{u4, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α' M _inst_3) (Finsupp.module.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4) (Finsupp.supported.{u4, u2, u3} α' M R _inst_1 _inst_3 _inst_4 t)))
Case conversion may be inaccurate. Consider using '#align finsupp.congr Finsupp.congrₓ'. -/
/-- An equivalence of sets induces a linear equivalence of `finsupp`s supported on those sets. -/
noncomputable def congr {α' : Type _} (s : Set α) (t : Set α') (e : s ≃ t) :
@@ -1350,7 +1350,7 @@ noncomputable def congr {α' : Type _} (s : Set α) (t : Set α') (e : s ≃ t)
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} [_inst_1 : Semiring.{u4} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5], (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) -> (LinearMap.{u4, u4, max u1 u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u1, u3} α N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u1, u3} α N _inst_5) (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u3, u4} α N R _inst_1 _inst_5 _inst_6))
but is expected to have type
- forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} [_inst_1 : Semiring.{u4} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5], (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) -> (LinearMap.{u4, u4, max u2 u1, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u1, u3} α N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u1, u3} α N _inst_5) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u4} α N R _inst_1 _inst_5 _inst_6))
+ forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} [_inst_1 : Semiring.{u4} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5], (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) -> (LinearMap.{u4, u4, max u2 u1, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u1, u3} α N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u1, u3} α N _inst_5) (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u3, u4} α N R _inst_1 _inst_5 _inst_6))
Case conversion may be inaccurate. Consider using '#align finsupp.map_range.linear_map Finsupp.mapRange.linearMapₓ'. -/
/-- `finsupp.map_range` as a `linear_map`. -/
@[simps]
@@ -1366,7 +1366,7 @@ def mapRange.linearMap (f : M →ₗ[R] N) : (α →₀ M) →ₗ[R] α →₀ N
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], Eq.{succ (max u1 u2)} (LinearMap.{u3, u3, max u1 u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.mapRange.linearMap.{u1, u2, u2, u3} α M M R _inst_1 _inst_3 _inst_4 _inst_3 _inst_4 (LinearMap.id.{u3, u2} R M _inst_1 _inst_3 _inst_4)) (LinearMap.id.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Eq.{max (succ u3) (succ u2)} (LinearMap.{u1, u1, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.mapRange.linearMap.{u3, u2, u2, u1} α M M R _inst_1 _inst_3 _inst_4 _inst_3 _inst_4 (LinearMap.id.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (LinearMap.id.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Eq.{max (succ u3) (succ u2)} (LinearMap.{u1, u1, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.mapRange.linearMap.{u3, u2, u2, u1} α M M R _inst_1 _inst_3 _inst_4 _inst_3 _inst_4 (LinearMap.id.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (LinearMap.id.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))
Case conversion may be inaccurate. Consider using '#align finsupp.map_range.linear_map_id Finsupp.mapRange.linearMap_idₓ'. -/
@[simp]
theorem mapRange.linearMap_id :
@@ -1378,7 +1378,7 @@ theorem mapRange.linearMap_id :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} {R : Type.{u5}} [_inst_1 : Semiring.{u5} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u5, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_7 : AddCommMonoid.{u4} P] [_inst_8 : Module.{u5, u4} R P _inst_1 _inst_7] (f : LinearMap.{u5, u5, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) N P _inst_5 _inst_7 _inst_6 _inst_8) (f₂ : LinearMap.{u5, u5, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6), Eq.{max (succ (max u1 u2)) (succ (max u1 u4))} (LinearMap.{u5, u5, max u1 u2, max u1 u4} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u1, u4} α P (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_7)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u1, u4} α P _inst_7) (Finsupp.module.{u1, u2, u5} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u4, u5} α P R _inst_1 _inst_7 _inst_8)) (Finsupp.mapRange.linearMap.{u1, u2, u4, u5} α M P R _inst_1 _inst_3 _inst_4 _inst_7 _inst_8 (LinearMap.comp.{u5, u5, u5, u2, u3, u4} R R R M N P _inst_1 _inst_1 _inst_1 _inst_3 _inst_5 _inst_7 _inst_4 _inst_6 _inst_8 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHomCompTriple.right_ids.{u5, u5} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) f f₂)) (LinearMap.comp.{u5, u5, u5, max u1 u2, max u1 u3, max u1 u4} R R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u1, u3} α N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)))) (Finsupp.{u1, u4} α P (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_7)))) _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u1, u3} α N _inst_5) (Finsupp.addCommMonoid.{u1, u4} α P _inst_7) (Finsupp.module.{u1, u2, u5} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u3, u5} α N R _inst_1 _inst_5 _inst_6) (Finsupp.module.{u1, u4, u5} α P R _inst_1 _inst_7 _inst_8) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHomCompTriple.right_ids.{u5, u5} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Finsupp.mapRange.linearMap.{u1, u3, u4, u5} α N P R _inst_1 _inst_5 _inst_6 _inst_7 _inst_8 f) (Finsupp.mapRange.linearMap.{u1, u2, u3, u5} α M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 f₂))
but is expected to have type
- forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u4}} {P : Type.{u3}} {R : Type.{u5}} [_inst_1 : Semiring.{u5} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u5, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u4} N] [_inst_6 : Module.{u5, u4} R N _inst_1 _inst_5] [_inst_7 : AddCommMonoid.{u3} P] [_inst_8 : Module.{u5, u3} R P _inst_1 _inst_7] (f : LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) N P _inst_5 _inst_7 _inst_6 _inst_8) (f₂ : LinearMap.{u5, u5, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6), Eq.{max (max (succ u1) (succ u2)) (succ u3)} (LinearMap.{u5, u5, max u2 u1, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u1, u3} α P (AddMonoid.toZero.{u3} P (AddCommMonoid.toAddMonoid.{u3} P _inst_7))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u1, u3} α P _inst_7) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u5} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u5} α P R _inst_1 _inst_7 _inst_8)) (Finsupp.mapRange.linearMap.{u1, u2, u3, u5} α M P R _inst_1 _inst_3 _inst_4 _inst_7 _inst_8 (LinearMap.comp.{u5, u5, u5, u2, u4, u3} R R R M N P _inst_1 _inst_1 _inst_1 _inst_3 _inst_5 _inst_7 _inst_4 _inst_6 _inst_8 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHomCompTriple.ids.{u5, u5} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) f f₂)) (LinearMap.comp.{u5, u5, u5, max u2 u1, max u4 u1, max u3 u1} R R R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u1, u4} α N (AddMonoid.toZero.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_5))) (Finsupp.{u1, u3} α P (AddMonoid.toZero.{u3} P (AddCommMonoid.toAddMonoid.{u3} P _inst_7))) _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u1, u4} α N _inst_5) (Finsupp.addCommMonoid.{u1, u3} α P _inst_7) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u5} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u4, u5} α N R _inst_1 _inst_5 _inst_6) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u5} α P R _inst_1 _inst_7 _inst_8) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHomCompTriple.ids.{u5, u5} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Finsupp.mapRange.linearMap.{u1, u4, u3, u5} α N P R _inst_1 _inst_5 _inst_6 _inst_7 _inst_8 f) (Finsupp.mapRange.linearMap.{u1, u2, u4, u5} α M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 f₂))
+ forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u4}} {P : Type.{u3}} {R : Type.{u5}} [_inst_1 : Semiring.{u5} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u5, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u4} N] [_inst_6 : Module.{u5, u4} R N _inst_1 _inst_5] [_inst_7 : AddCommMonoid.{u3} P] [_inst_8 : Module.{u5, u3} R P _inst_1 _inst_7] (f : LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) N P _inst_5 _inst_7 _inst_6 _inst_8) (f₂ : LinearMap.{u5, u5, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6), Eq.{max (max (succ u1) (succ u2)) (succ u3)} (LinearMap.{u5, u5, max u2 u1, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u1, u3} α P (AddMonoid.toZero.{u3} P (AddCommMonoid.toAddMonoid.{u3} P _inst_7))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u1, u3} α P _inst_7) (Finsupp.module.{u1, u2, u5} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u3, u5} α P R _inst_1 _inst_7 _inst_8)) (Finsupp.mapRange.linearMap.{u1, u2, u3, u5} α M P R _inst_1 _inst_3 _inst_4 _inst_7 _inst_8 (LinearMap.comp.{u5, u5, u5, u2, u4, u3} R R R M N P _inst_1 _inst_1 _inst_1 _inst_3 _inst_5 _inst_7 _inst_4 _inst_6 _inst_8 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHomCompTriple.ids.{u5, u5} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) f f₂)) (LinearMap.comp.{u5, u5, u5, max u2 u1, max u4 u1, max u3 u1} R R R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u1, u4} α N (AddMonoid.toZero.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_5))) (Finsupp.{u1, u3} α P (AddMonoid.toZero.{u3} P (AddCommMonoid.toAddMonoid.{u3} P _inst_7))) _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u1, u4} α N _inst_5) (Finsupp.addCommMonoid.{u1, u3} α P _inst_7) (Finsupp.module.{u1, u2, u5} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u4, u5} α N R _inst_1 _inst_5 _inst_6) (Finsupp.module.{u1, u3, u5} α P R _inst_1 _inst_7 _inst_8) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHomCompTriple.ids.{u5, u5} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Finsupp.mapRange.linearMap.{u1, u4, u3, u5} α N P R _inst_1 _inst_5 _inst_6 _inst_7 _inst_8 f) (Finsupp.mapRange.linearMap.{u1, u2, u4, u5} α M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 f₂))
Case conversion may be inaccurate. Consider using '#align finsupp.map_range.linear_map_comp Finsupp.mapRange.linearMap_compₓ'. -/
theorem mapRange.linearMap_comp (f : N →ₗ[R] P) (f₂ : M →ₗ[R] N) :
(mapRange.linearMap (f.comp f₂) : (α →₀ _) →ₗ[R] _) =
@@ -1390,7 +1390,7 @@ theorem mapRange.linearMap_comp (f : N →ₗ[R] P) (f₂ : M →ₗ[R] N) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} [_inst_1 : Semiring.{u4} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] (f : LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6), Eq.{max (succ (max u1 u3)) (succ (max u1 u2))} (AddMonoidHom.{max u1 u2, max u1 u3} (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u1, u3} α N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)))) (AddMonoid.toAddZeroClass.{max u1 u2} (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3))) (AddMonoid.toAddZeroClass.{max u1 u3} (Finsupp.{u1, u3} α N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u1, u3} α N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)))) (Finsupp.addCommMonoid.{u1, u3} α N _inst_5)))) (LinearMap.toAddMonoidHom.{u4, u4, max u1 u2, max u1 u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u1, u3} α N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u1, u3} α N _inst_5) (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u3, u4} α N R _inst_1 _inst_5 _inst_6) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.mapRange.linearMap.{u1, u2, u3, u4} α M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 f)) (Finsupp.mapRange.addMonoidHom.{u1, u2, u3} α M N _inst_3 _inst_5 (LinearMap.toAddMonoidHom.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) f))
but is expected to have type
- forall {α : Type.{u1}} {M : Type.{u3}} {N : Type.{u2}} {R : Type.{u4}} [_inst_1 : Semiring.{u4} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u4, u3} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : Module.{u4, u2} R N _inst_1 _inst_5] (f : LinearMap.{u4, u4, u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6), Eq.{max (max (succ u1) (succ u3)) (succ u2)} (AddMonoidHom.{max u3 u1, max u2 u1} (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u1, u2} α N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))) (AddMonoid.toAddZeroClass.{max u3 u1} (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (AddCommMonoid.toAddMonoid.{max u3 u1} (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.addCommMonoid.{u1, u3} α M _inst_3))) (AddMonoid.toAddZeroClass.{max u2 u1} (Finsupp.{u1, u2} α N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Finsupp.{u1, u2} α N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))) (Finsupp.addCommMonoid.{u1, u2} α N _inst_5)))) (LinearMap.toAddMonoidHom.{u4, u4, max u3 u1, max u2 u1} R R (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u1, u2} α N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α M _inst_3) (Finsupp.addCommMonoid.{u1, u2} α N _inst_5) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u4} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u4} α N R _inst_1 _inst_5 _inst_6) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.mapRange.linearMap.{u1, u3, u2, u4} α M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 f)) (Finsupp.mapRange.addMonoidHom.{u1, u3, u2} α M N _inst_3 _inst_5 (LinearMap.toAddMonoidHom.{u4, u4, u3, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) f))
+ forall {α : Type.{u1}} {M : Type.{u3}} {N : Type.{u2}} {R : Type.{u4}} [_inst_1 : Semiring.{u4} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u4, u3} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : Module.{u4, u2} R N _inst_1 _inst_5] (f : LinearMap.{u4, u4, u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6), Eq.{max (max (succ u1) (succ u3)) (succ u2)} (AddMonoidHom.{max u3 u1, max u2 u1} (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u1, u2} α N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))) (AddMonoid.toAddZeroClass.{max u3 u1} (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (AddCommMonoid.toAddMonoid.{max u3 u1} (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.addCommMonoid.{u1, u3} α M _inst_3))) (AddMonoid.toAddZeroClass.{max u2 u1} (Finsupp.{u1, u2} α N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Finsupp.{u1, u2} α N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))) (Finsupp.addCommMonoid.{u1, u2} α N _inst_5)))) (LinearMap.toAddMonoidHom.{u4, u4, max u3 u1, max u2 u1} R R (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u1, u2} α N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α M _inst_3) (Finsupp.addCommMonoid.{u1, u2} α N _inst_5) (Finsupp.module.{u1, u3, u4} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u2, u4} α N R _inst_1 _inst_5 _inst_6) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.mapRange.linearMap.{u1, u3, u2, u4} α M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 f)) (Finsupp.mapRange.addMonoidHom.{u1, u3, u2} α M N _inst_3 _inst_5 (LinearMap.toAddMonoidHom.{u4, u4, u3, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) f))
Case conversion may be inaccurate. Consider using '#align finsupp.map_range.linear_map_to_add_monoid_hom Finsupp.mapRange.linearMap_toAddMonoidHomₓ'. -/
@[simp]
theorem mapRange.linearMap_toAddMonoidHom (f : M →ₗ[R] N) :
@@ -1403,7 +1403,7 @@ theorem mapRange.linearMap_toAddMonoidHom (f : M →ₗ[R] N) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} [_inst_1 : Semiring.{u4} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5], (LinearEquiv.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R _inst_1) (RingHomInvPair.ids.{u4} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) -> (LinearEquiv.{u4, u4, max u1 u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R _inst_1) (RingHomInvPair.ids.{u4} R _inst_1) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u1, u3} α N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u1, u3} α N _inst_5) (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u3, u4} α N R _inst_1 _inst_5 _inst_6))
but is expected to have type
- forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} [_inst_1 : Semiring.{u4} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5], (LinearEquiv.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R _inst_1) (RingHomInvPair.ids.{u4} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) -> (LinearEquiv.{u4, u4, max u2 u1, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R _inst_1) (RingHomInvPair.ids.{u4} R _inst_1) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u1, u3} α N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u1, u3} α N _inst_5) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u4} α N R _inst_1 _inst_5 _inst_6))
+ forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} [_inst_1 : Semiring.{u4} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5], (LinearEquiv.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R _inst_1) (RingHomInvPair.ids.{u4} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) -> (LinearEquiv.{u4, u4, max u2 u1, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R _inst_1) (RingHomInvPair.ids.{u4} R _inst_1) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u1, u3} α N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u1, u3} α N _inst_5) (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u3, u4} α N R _inst_1 _inst_5 _inst_6))
Case conversion may be inaccurate. Consider using '#align finsupp.map_range.linear_equiv Finsupp.mapRange.linearEquivₓ'. -/
/-- `finsupp.map_range` as a `linear_equiv`. -/
@[simps apply]
@@ -1418,7 +1418,7 @@ def mapRange.linearEquiv (e : M ≃ₗ[R] N) : (α →₀ M) ≃ₗ[R] α →₀
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], Eq.{succ (max u1 u2)} (LinearEquiv.{u3, u3, max u1 u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.mapRange.linearEquiv.{u1, u2, u2, u3} α M M R _inst_1 _inst_3 _inst_4 _inst_3 _inst_4 (LinearEquiv.refl.{u3, u2} R M _inst_1 _inst_3 _inst_4)) (LinearEquiv.refl.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Eq.{max (succ u3) (succ u2)} (LinearEquiv.{u1, u1, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.mapRange.linearEquiv.{u3, u2, u2, u1} α M M R _inst_1 _inst_3 _inst_4 _inst_3 _inst_4 (LinearEquiv.refl.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (LinearEquiv.refl.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Eq.{max (succ u3) (succ u2)} (LinearEquiv.{u1, u1, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.mapRange.linearEquiv.{u3, u2, u2, u1} α M M R _inst_1 _inst_3 _inst_4 _inst_3 _inst_4 (LinearEquiv.refl.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (LinearEquiv.refl.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.module.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))
Case conversion may be inaccurate. Consider using '#align finsupp.map_range.linear_equiv_refl Finsupp.mapRange.linearEquiv_reflₓ'. -/
@[simp]
theorem mapRange.linearEquiv_refl :
@@ -1430,7 +1430,7 @@ theorem mapRange.linearEquiv_refl :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} {R : Type.{u5}} [_inst_1 : Semiring.{u5} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u5, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_7 : AddCommMonoid.{u4} P] [_inst_8 : Module.{u5, u4} R P _inst_1 _inst_7] (f : LinearEquiv.{u5, u5, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (f₂ : LinearEquiv.{u5, u5, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) N P _inst_5 _inst_7 _inst_6 _inst_8), Eq.{max (succ (max u1 u2)) (succ (max u1 u4))} (LinearEquiv.{u5, u5, max u1 u2, max u1 u4} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u1, u4} α P (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_7)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u1, u4} α P _inst_7) (Finsupp.module.{u1, u2, u5} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u4, u5} α P R _inst_1 _inst_7 _inst_8)) (Finsupp.mapRange.linearEquiv.{u1, u2, u4, u5} α M P R _inst_1 _inst_3 _inst_4 _inst_7 _inst_8 (LinearEquiv.trans.{u5, u5, u5, u2, u3, u4} R R R M N P _inst_1 _inst_1 _inst_1 _inst_3 _inst_5 _inst_7 _inst_4 _inst_6 _inst_8 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHomCompTriple.right_ids.{u5, u5} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (RingHomCompTriple.right_ids.{u5, u5} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) f f₂)) (LinearEquiv.trans.{u5, u5, u5, max u1 u2, max u1 u3, max u1 u4} R R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u1, u3} α N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)))) (Finsupp.{u1, u4} α P (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_7)))) _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u1, u3} α N _inst_5) (Finsupp.addCommMonoid.{u1, u4} α P _inst_7) (Finsupp.module.{u1, u2, u5} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u3, u5} α N R _inst_1 _inst_5 _inst_6) (Finsupp.module.{u1, u4, u5} α P R _inst_1 _inst_7 _inst_8) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHomCompTriple.right_ids.{u5, u5} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (RingHomCompTriple.right_ids.{u5, u5} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) (Finsupp.mapRange.linearEquiv.{u1, u2, u3, u5} α M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 f) (Finsupp.mapRange.linearEquiv.{u1, u3, u4, u5} α N P R _inst_1 _inst_5 _inst_6 _inst_7 _inst_8 f₂))
but is expected to have type
- forall {α : Type.{u1}} {M : Type.{u4}} {N : Type.{u3}} {P : Type.{u2}} {R : Type.{u5}} [_inst_1 : Semiring.{u5} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_7 : AddCommMonoid.{u2} P] [_inst_8 : Module.{u5, u2} R P _inst_1 _inst_7] (f : LinearEquiv.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (f₂ : LinearEquiv.{u5, u5, u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) N P _inst_5 _inst_7 _inst_6 _inst_8), Eq.{max (max (succ u1) (succ u4)) (succ u2)} (LinearEquiv.{u5, u5, max u4 u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) (Finsupp.{u1, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (Finsupp.{u1, u2} α P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_7))) (Finsupp.addCommMonoid.{u1, u4} α M _inst_3) (Finsupp.addCommMonoid.{u1, u2} α P _inst_7) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u4, u5} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u5} α P R _inst_1 _inst_7 _inst_8)) (Finsupp.mapRange.linearEquiv.{u1, u4, u2, u5} α M P R _inst_1 _inst_3 _inst_4 _inst_7 _inst_8 (LinearEquiv.trans.{u5, u5, u5, u4, u3, u2} R R R M N P _inst_1 _inst_1 _inst_1 _inst_3 _inst_5 _inst_7 _inst_4 _inst_6 _inst_8 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHomCompTriple.ids.{u5, u5} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (RingHomCompTriple.ids.{u5, u5} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) f f₂)) (LinearEquiv.trans.{u5, u5, u5, max u4 u1, max u3 u1, max u2 u1} R R R (Finsupp.{u1, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (Finsupp.{u1, u3} α N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Finsupp.{u1, u2} α P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_7))) _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u4} α M _inst_3) (Finsupp.addCommMonoid.{u1, u3} α N _inst_5) (Finsupp.addCommMonoid.{u1, u2} α P _inst_7) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u4, u5} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u5} α N R _inst_1 _inst_5 _inst_6) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u5} α P R _inst_1 _inst_7 _inst_8) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHomCompTriple.ids.{u5, u5} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (RingHomCompTriple.ids.{u5, u5} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) (Finsupp.mapRange.linearEquiv.{u1, u4, u3, u5} α M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 f) (Finsupp.mapRange.linearEquiv.{u1, u3, u2, u5} α N P R _inst_1 _inst_5 _inst_6 _inst_7 _inst_8 f₂))
+ forall {α : Type.{u1}} {M : Type.{u4}} {N : Type.{u3}} {P : Type.{u2}} {R : Type.{u5}} [_inst_1 : Semiring.{u5} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_7 : AddCommMonoid.{u2} P] [_inst_8 : Module.{u5, u2} R P _inst_1 _inst_7] (f : LinearEquiv.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (f₂ : LinearEquiv.{u5, u5, u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) N P _inst_5 _inst_7 _inst_6 _inst_8), Eq.{max (max (succ u1) (succ u4)) (succ u2)} (LinearEquiv.{u5, u5, max u4 u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) (Finsupp.{u1, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (Finsupp.{u1, u2} α P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_7))) (Finsupp.addCommMonoid.{u1, u4} α M _inst_3) (Finsupp.addCommMonoid.{u1, u2} α P _inst_7) (Finsupp.module.{u1, u4, u5} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u2, u5} α P R _inst_1 _inst_7 _inst_8)) (Finsupp.mapRange.linearEquiv.{u1, u4, u2, u5} α M P R _inst_1 _inst_3 _inst_4 _inst_7 _inst_8 (LinearEquiv.trans.{u5, u5, u5, u4, u3, u2} R R R M N P _inst_1 _inst_1 _inst_1 _inst_3 _inst_5 _inst_7 _inst_4 _inst_6 _inst_8 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHomCompTriple.ids.{u5, u5} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (RingHomCompTriple.ids.{u5, u5} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) f f₂)) (LinearEquiv.trans.{u5, u5, u5, max u4 u1, max u3 u1, max u2 u1} R R R (Finsupp.{u1, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (Finsupp.{u1, u3} α N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Finsupp.{u1, u2} α P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_7))) _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u4} α M _inst_3) (Finsupp.addCommMonoid.{u1, u3} α N _inst_5) (Finsupp.addCommMonoid.{u1, u2} α P _inst_7) (Finsupp.module.{u1, u4, u5} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u3, u5} α N R _inst_1 _inst_5 _inst_6) (Finsupp.module.{u1, u2, u5} α P R _inst_1 _inst_7 _inst_8) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHomCompTriple.ids.{u5, u5} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (RingHomCompTriple.ids.{u5, u5} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) (RingHomInvPair.ids.{u5} R _inst_1) (Finsupp.mapRange.linearEquiv.{u1, u4, u3, u5} α M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 f) (Finsupp.mapRange.linearEquiv.{u1, u3, u2, u5} α N P R _inst_1 _inst_5 _inst_6 _inst_7 _inst_8 f₂))
Case conversion may be inaccurate. Consider using '#align finsupp.map_range.linear_equiv_trans Finsupp.mapRange.linearEquiv_transₓ'. -/
theorem mapRange.linearEquiv_trans (f : M ≃ₗ[R] N) (f₂ : N ≃ₗ[R] P) :
(mapRange.linearEquiv (f.trans f₂) : (α →₀ _) ≃ₗ[R] _) =
@@ -1442,7 +1442,7 @@ theorem mapRange.linearEquiv_trans (f : M ≃ₗ[R] N) (f₂ : N ≃ₗ[R] P) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} [_inst_1 : Semiring.{u4} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] (f : LinearEquiv.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R _inst_1) (RingHomInvPair.ids.{u4} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6), Eq.{max (succ (max u1 u3)) (succ (max u1 u2))} (LinearEquiv.{u4, u4, max u1 u3, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R _inst_1) (RingHomInvPair.ids.{u4} R _inst_1) (Finsupp.{u1, u3} α N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)))) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.addCommMonoid.{u1, u3} α N _inst_5) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u3, u4} α N R _inst_1 _inst_5 _inst_6) (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4)) (LinearEquiv.symm.{u4, u4, max u1 u2, max u1 u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u1, u3} α N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u1, u3} α N _inst_5) (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u3, u4} α N R _inst_1 _inst_5 _inst_6) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R _inst_1) (RingHomInvPair.ids.{u4} R _inst_1) (Finsupp.mapRange.linearEquiv.{u1, u2, u3, u4} α M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 f)) (Finsupp.mapRange.linearEquiv.{u1, u3, u2, u4} α N M R _inst_1 _inst_5 _inst_6 _inst_3 _inst_4 (LinearEquiv.symm.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R _inst_1) (RingHomInvPair.ids.{u4} R _inst_1) f))
but is expected to have type
- forall {α : Type.{u1}} {M : Type.{u3}} {N : Type.{u2}} {R : Type.{u4}} [_inst_1 : Semiring.{u4} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u4, u3} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : Module.{u4, u2} R N _inst_1 _inst_5] (f : LinearEquiv.{u4, u4, u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R _inst_1) (RingHomInvPair.ids.{u4} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6), Eq.{max (max (succ u1) (succ u3)) (succ u2)} (LinearEquiv.{u4, u4, max u2 u1, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R _inst_1) (RingHomInvPair.ids.{u4} R _inst_1) (Finsupp.{u1, u2} α N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))) (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.addCommMonoid.{u1, u2} α N _inst_5) (Finsupp.addCommMonoid.{u1, u3} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u4} α N R _inst_1 _inst_5 _inst_6) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u4} α M R _inst_1 _inst_3 _inst_4)) (LinearEquiv.symm.{u4, u4, max u3 u1, max u2 u1} R R (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u1, u2} α N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α M _inst_3) (Finsupp.addCommMonoid.{u1, u2} α N _inst_5) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u4} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u4} α N R _inst_1 _inst_5 _inst_6) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R _inst_1) (RingHomInvPair.ids.{u4} R _inst_1) (Finsupp.mapRange.linearEquiv.{u1, u3, u2, u4} α M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 f)) (Finsupp.mapRange.linearEquiv.{u1, u2, u3, u4} α N M R _inst_1 _inst_5 _inst_6 _inst_3 _inst_4 (LinearEquiv.symm.{u4, u4, u3, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R _inst_1) (RingHomInvPair.ids.{u4} R _inst_1) f))
+ forall {α : Type.{u1}} {M : Type.{u3}} {N : Type.{u2}} {R : Type.{u4}} [_inst_1 : Semiring.{u4} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u4, u3} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : Module.{u4, u2} R N _inst_1 _inst_5] (f : LinearEquiv.{u4, u4, u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R _inst_1) (RingHomInvPair.ids.{u4} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6), Eq.{max (max (succ u1) (succ u3)) (succ u2)} (LinearEquiv.{u4, u4, max u2 u1, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R _inst_1) (RingHomInvPair.ids.{u4} R _inst_1) (Finsupp.{u1, u2} α N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))) (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.addCommMonoid.{u1, u2} α N _inst_5) (Finsupp.addCommMonoid.{u1, u3} α M _inst_3) (Finsupp.module.{u1, u2, u4} α N R _inst_1 _inst_5 _inst_6) (Finsupp.module.{u1, u3, u4} α M R _inst_1 _inst_3 _inst_4)) (LinearEquiv.symm.{u4, u4, max u3 u1, max u2 u1} R R (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u1, u2} α N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α M _inst_3) (Finsupp.addCommMonoid.{u1, u2} α N _inst_5) (Finsupp.module.{u1, u3, u4} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u2, u4} α N R _inst_1 _inst_5 _inst_6) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R _inst_1) (RingHomInvPair.ids.{u4} R _inst_1) (Finsupp.mapRange.linearEquiv.{u1, u3, u2, u4} α M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 f)) (Finsupp.mapRange.linearEquiv.{u1, u2, u3, u4} α N M R _inst_1 _inst_5 _inst_6 _inst_3 _inst_4 (LinearEquiv.symm.{u4, u4, u3, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R _inst_1) (RingHomInvPair.ids.{u4} R _inst_1) f))
Case conversion may be inaccurate. Consider using '#align finsupp.map_range.linear_equiv_symm Finsupp.mapRange.linearEquiv_symmₓ'. -/
@[simp]
theorem mapRange.linearEquiv_symm (f : M ≃ₗ[R] N) :
@@ -1454,7 +1454,7 @@ theorem mapRange.linearEquiv_symm (f : M ≃ₗ[R] N) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} [_inst_1 : Semiring.{u4} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] (f : LinearEquiv.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R _inst_1) (RingHomInvPair.ids.{u4} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6), Eq.{max (succ (max u1 u2)) (succ (max u1 u3))} (AddEquiv.{max u1 u2, max u1 u3} (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u1, u3} α N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)))) (AddZeroClass.toHasAdd.{max u1 u2} (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (AddMonoid.toAddZeroClass.{max u1 u2} (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3)))) (AddZeroClass.toHasAdd.{max u1 u3} (Finsupp.{u1, u3} α N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)))) (AddMonoid.toAddZeroClass.{max u1 u3} (Finsupp.{u1, u3} α N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u1, u3} α N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)))) (Finsupp.addCommMonoid.{u1, u3} α N _inst_5))))) (LinearEquiv.toAddEquiv.{u4, u4, max u1 u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R _inst_1) (RingHomInvPair.ids.{u4} R _inst_1) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u1, u3} α N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u1, u3} α N _inst_5) (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u3, u4} α N R _inst_1 _inst_5 _inst_6) (Finsupp.mapRange.linearEquiv.{u1, u2, u3, u4} α M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 f)) (Finsupp.mapRange.addEquiv.{u1, u2, u3} α M N _inst_3 _inst_5 (LinearEquiv.toAddEquiv.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R _inst_1) (RingHomInvPair.ids.{u4} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6 f))
but is expected to have type
- forall {α : Type.{u1}} {M : Type.{u3}} {N : Type.{u2}} {R : Type.{u4}} [_inst_1 : Semiring.{u4} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u4, u3} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : Module.{u4, u2} R N _inst_1 _inst_5] (f : LinearEquiv.{u4, u4, u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R _inst_1) (RingHomInvPair.ids.{u4} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6), Eq.{max (max (succ u1) (succ u3)) (succ u2)} (AddEquiv.{max u3 u1, max u2 u1} (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u1, u2} α N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))) (AddZeroClass.toAdd.{max u3 u1} (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (AddMonoid.toAddZeroClass.{max u3 u1} (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (AddCommMonoid.toAddMonoid.{max u3 u1} (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.addCommMonoid.{u1, u3} α M _inst_3)))) (AddZeroClass.toAdd.{max u2 u1} (Finsupp.{u1, u2} α N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))) (AddMonoid.toAddZeroClass.{max u2 u1} (Finsupp.{u1, u2} α N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Finsupp.{u1, u2} α N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))) (Finsupp.addCommMonoid.{u1, u2} α N _inst_5))))) (LinearEquiv.toAddEquiv.{u4, u4, max u3 u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R _inst_1) (RingHomInvPair.ids.{u4} R _inst_1) (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u1, u2} α N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))) (Finsupp.addCommMonoid.{u1, u3} α M _inst_3) (Finsupp.addCommMonoid.{u1, u2} α N _inst_5) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u4} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u4} α N R _inst_1 _inst_5 _inst_6) (Finsupp.mapRange.linearEquiv.{u1, u3, u2, u4} α M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 f)) (Finsupp.mapRange.addEquiv.{u1, u3, u2} α M N _inst_3 _inst_5 (LinearEquiv.toAddEquiv.{u4, u4, u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R _inst_1) (RingHomInvPair.ids.{u4} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6 f))
+ forall {α : Type.{u1}} {M : Type.{u3}} {N : Type.{u2}} {R : Type.{u4}} [_inst_1 : Semiring.{u4} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u4, u3} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : Module.{u4, u2} R N _inst_1 _inst_5] (f : LinearEquiv.{u4, u4, u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R _inst_1) (RingHomInvPair.ids.{u4} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6), Eq.{max (max (succ u1) (succ u3)) (succ u2)} (AddEquiv.{max u3 u1, max u2 u1} (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u1, u2} α N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))) (AddZeroClass.toAdd.{max u3 u1} (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (AddMonoid.toAddZeroClass.{max u3 u1} (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (AddCommMonoid.toAddMonoid.{max u3 u1} (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.addCommMonoid.{u1, u3} α M _inst_3)))) (AddZeroClass.toAdd.{max u2 u1} (Finsupp.{u1, u2} α N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))) (AddMonoid.toAddZeroClass.{max u2 u1} (Finsupp.{u1, u2} α N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Finsupp.{u1, u2} α N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))) (Finsupp.addCommMonoid.{u1, u2} α N _inst_5))))) (LinearEquiv.toAddEquiv.{u4, u4, max u3 u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R _inst_1) (RingHomInvPair.ids.{u4} R _inst_1) (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u1, u2} α N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))) (Finsupp.addCommMonoid.{u1, u3} α M _inst_3) (Finsupp.addCommMonoid.{u1, u2} α N _inst_5) (Finsupp.module.{u1, u3, u4} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u2, u4} α N R _inst_1 _inst_5 _inst_6) (Finsupp.mapRange.linearEquiv.{u1, u3, u2, u4} α M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 f)) (Finsupp.mapRange.addEquiv.{u1, u3, u2} α M N _inst_3 _inst_5 (LinearEquiv.toAddEquiv.{u4, u4, u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R _inst_1) (RingHomInvPair.ids.{u4} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6 f))
Case conversion may be inaccurate. Consider using '#align finsupp.map_range.linear_equiv_to_add_equiv Finsupp.mapRange.linearEquiv_toAddEquivₓ'. -/
@[simp]
theorem mapRange.linearEquiv_toAddEquiv (f : M ≃ₗ[R] N) :
@@ -1466,7 +1466,7 @@ theorem mapRange.linearEquiv_toAddEquiv (f : M ≃ₗ[R] N) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} [_inst_1 : Semiring.{u4} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] (f : LinearEquiv.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R _inst_1) (RingHomInvPair.ids.{u4} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6), Eq.{max (succ (max u1 u2)) (succ (max u1 u3))} (LinearMap.{u4, u4, max u1 u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u1, u3} α N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u1, u3} α N _inst_5) (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u3, u4} α N R _inst_1 _inst_5 _inst_6)) (LinearEquiv.toLinearMap.{u4, u4, max u1 u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R _inst_1) (RingHomInvPair.ids.{u4} R _inst_1) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{u1, u3} α N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)))) (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.addCommMonoid.{u1, u3} α N _inst_5) (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u3, u4} α N R _inst_1 _inst_5 _inst_6) (Finsupp.mapRange.linearEquiv.{u1, u2, u3, u4} α M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 f)) (Finsupp.mapRange.linearMap.{u1, u2, u3, u4} α M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 (LinearEquiv.toLinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R _inst_1) (RingHomInvPair.ids.{u4} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6 f))
but is expected to have type
- forall {α : Type.{u1}} {M : Type.{u3}} {N : Type.{u2}} {R : Type.{u4}} [_inst_1 : Semiring.{u4} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u4, u3} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : Module.{u4, u2} R N _inst_1 _inst_5] (f : LinearEquiv.{u4, u4, u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R _inst_1) (RingHomInvPair.ids.{u4} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6), Eq.{max (max (succ u1) (succ u3)) (succ u2)} (LinearMap.{u4, u4, max u3 u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u1, u2} α N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))) (Finsupp.addCommMonoid.{u1, u3} α M _inst_3) (Finsupp.addCommMonoid.{u1, u2} α N _inst_5) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u4} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u4} α N R _inst_1 _inst_5 _inst_6)) (LinearEquiv.toLinearMap.{u4, u4, max u3 u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R _inst_1) (RingHomInvPair.ids.{u4} R _inst_1) (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u1, u2} α N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))) (Finsupp.addCommMonoid.{u1, u3} α M _inst_3) (Finsupp.addCommMonoid.{u1, u2} α N _inst_5) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u4} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u4} α N R _inst_1 _inst_5 _inst_6) (Finsupp.mapRange.linearEquiv.{u1, u3, u2, u4} α M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 f)) (Finsupp.mapRange.linearMap.{u1, u3, u2, u4} α M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 (LinearEquiv.toLinearMap.{u4, u4, u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R _inst_1) (RingHomInvPair.ids.{u4} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6 f))
+ forall {α : Type.{u1}} {M : Type.{u3}} {N : Type.{u2}} {R : Type.{u4}} [_inst_1 : Semiring.{u4} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u4, u3} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : Module.{u4, u2} R N _inst_1 _inst_5] (f : LinearEquiv.{u4, u4, u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R _inst_1) (RingHomInvPair.ids.{u4} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6), Eq.{max (max (succ u1) (succ u3)) (succ u2)} (LinearMap.{u4, u4, max u3 u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u1, u2} α N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))) (Finsupp.addCommMonoid.{u1, u3} α M _inst_3) (Finsupp.addCommMonoid.{u1, u2} α N _inst_5) (Finsupp.module.{u1, u3, u4} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u2, u4} α N R _inst_1 _inst_5 _inst_6)) (LinearEquiv.toLinearMap.{u4, u4, max u3 u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R _inst_1) (RingHomInvPair.ids.{u4} R _inst_1) (Finsupp.{u1, u3} α M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Finsupp.{u1, u2} α N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))) (Finsupp.addCommMonoid.{u1, u3} α M _inst_3) (Finsupp.addCommMonoid.{u1, u2} α N _inst_5) (Finsupp.module.{u1, u3, u4} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u1, u2, u4} α N R _inst_1 _inst_5 _inst_6) (Finsupp.mapRange.linearEquiv.{u1, u3, u2, u4} α M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 f)) (Finsupp.mapRange.linearMap.{u1, u3, u2, u4} α M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 (LinearEquiv.toLinearMap.{u4, u4, u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R _inst_1) (RingHomInvPair.ids.{u4} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6 f))
Case conversion may be inaccurate. Consider using '#align finsupp.map_range.linear_equiv_to_linear_map Finsupp.mapRange.linearEquiv_toLinearMapₓ'. -/
@[simp]
theorem mapRange.linearEquiv_toLinearMap (f : M ≃ₗ[R] N) :
@@ -1478,7 +1478,7 @@ theorem mapRange.linearEquiv_toLinearMap (f : M ≃ₗ[R] N) :
lean 3 declaration is
forall {M : Type.{u1}} {N : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : Module.{u3, u2} R N _inst_1 _inst_5] {ι : Type.{u4}} {κ : Type.{u5}}, (Equiv.{succ u4, succ u5} ι κ) -> (LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) -> (LinearEquiv.{u3, u3, max u4 u1, max u5 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) (Finsupp.addCommMonoid.{u4, u1} ι M _inst_3) (Finsupp.addCommMonoid.{u5, u2} κ N _inst_5) (Finsupp.module.{u4, u1, u3} ι M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u5, u2, u3} κ N R _inst_1 _inst_5 _inst_6))
but is expected to have type
- forall {M : Type.{u1}} {N : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : Module.{u3, u2} R N _inst_1 _inst_5] {ι : Type.{u4}} {κ : Type.{u5}}, (Equiv.{succ u4, succ u5} ι κ) -> (LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) -> (LinearEquiv.{u3, u3, max u1 u4, max u2 u5} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.{u4, u1} ι M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Finsupp.{u5, u2} κ N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))) (Finsupp.addCommMonoid.{u4, u1} ι M _inst_3) (Finsupp.addCommMonoid.{u5, u2} κ N _inst_5) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u1, u3} ι M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u5, u2, u3} κ N R _inst_1 _inst_5 _inst_6))
+ forall {M : Type.{u1}} {N : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : Module.{u3, u2} R N _inst_1 _inst_5] {ι : Type.{u4}} {κ : Type.{u5}}, (Equiv.{succ u4, succ u5} ι κ) -> (LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) -> (LinearEquiv.{u3, u3, max u1 u4, max u2 u5} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.{u4, u1} ι M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Finsupp.{u5, u2} κ N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))) (Finsupp.addCommMonoid.{u4, u1} ι M _inst_3) (Finsupp.addCommMonoid.{u5, u2} κ N _inst_5) (Finsupp.module.{u4, u1, u3} ι M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u5, u2, u3} κ N R _inst_1 _inst_5 _inst_6))
Case conversion may be inaccurate. Consider using '#align finsupp.lcongr Finsupp.lcongrₓ'. -/
/-- An equivalence of domain and a linear equivalence of codomain induce a linear equivalence of the
corresponding finitely supported functions. -/
@@ -1490,7 +1490,7 @@ def lcongr {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N) : (ι →
lean 3 declaration is
forall {M : Type.{u1}} {N : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : Module.{u3, u2} R N _inst_1 _inst_5] {ι : Type.{u4}} {κ : Type.{u5}} (e₁ : Equiv.{succ u4, succ u5} ι κ) (e₂ : LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (i : ι) (m : M), Eq.{max (succ u5) (succ u2)} (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) (coeFn.{max (succ (max u4 u1)) (succ (max u5 u2)), max (succ (max u4 u1)) (succ (max u5 u2))} (LinearEquiv.{u3, u3, max u4 u1, max u5 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) (Finsupp.addCommMonoid.{u4, u1} ι M _inst_3) (Finsupp.addCommMonoid.{u5, u2} κ N _inst_5) (Finsupp.module.{u4, u1, u3} ι M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u5, u2, u3} κ N R _inst_1 _inst_5 _inst_6)) (fun (_x : LinearEquiv.{u3, u3, max u4 u1, max u5 u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) (Finsupp.addCommMonoid.{u4, u1} ι M _inst_3) (Finsupp.addCommMonoid.{u5, u2} κ N _inst_5) (Finsupp.module.{u4, u1, u3} ι M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u5, u2, u3} κ N R _inst_1 _inst_5 _inst_6)) => (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) -> (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))))) (LinearEquiv.hasCoeToFun.{u3, u3, max u4 u1, max u5 u2} R R (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u1} ι M _inst_3) (Finsupp.addCommMonoid.{u5, u2} κ N _inst_5) (Finsupp.module.{u4, u1, u3} ι M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u5, u2, u3} κ N R _inst_1 _inst_5 _inst_6) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)) (Finsupp.lcongr.{u1, u2, u3, u4, u5} M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 ι κ e₁ e₂) (Finsupp.single.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) i m)) (Finsupp.single.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))) (coeFn.{max 1 (max (succ u4) (succ u5)) (succ u5) (succ u4), max (succ u4) (succ u5)} (Equiv.{succ u4, succ u5} ι κ) (fun (_x : Equiv.{succ u4, succ u5} ι κ) => ι -> κ) (Equiv.hasCoeToFun.{succ u4, succ u5} ι κ) e₁ i) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (_x : LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) => M -> N) (LinearEquiv.hasCoeToFun.{u3, u3, u1, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)) e₂ m))
but is expected to have type
- forall {M : Type.{u2}} {N : Type.{u1}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : Module.{u3, u1} R N _inst_1 _inst_5] {ι : Type.{u5}} {κ : Type.{u4}} (e₁ : Equiv.{succ u5, succ u4} ι κ) (e₂ : LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (i : ι) (m : M), Eq.{max (succ u1) (succ u4)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (Finsupp.single.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) i m)) (FunLike.coe.{max (max (max (succ u2) (succ u1)) (succ u4)) (succ u5), max (succ u2) (succ u5), max (succ u1) (succ u4)} (LinearEquiv.{u3, u3, max u2 u5, max u1 u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (Finsupp.addCommMonoid.{u5, u2} ι M _inst_3) (Finsupp.addCommMonoid.{u4, u1} κ N _inst_5) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u5, u2, u3} ι M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u1, u3} κ N R _inst_1 _inst_5 _inst_6)) (Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (fun (_x : Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) _x) (SMulHomClass.toFunLike.{max (max (max u2 u1) u4) u5, u3, max u2 u5, max u1 u4} (LinearEquiv.{u3, u3, max u2 u5, max u1 u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (Finsupp.addCommMonoid.{u5, u2} ι M _inst_3) (Finsupp.addCommMonoid.{u4, u1} κ N _inst_5) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u5, 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e₁ i) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M) => N) _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) R M N (SMulZeroClass.toSMul.{u3, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (DistribSMul.toSMulZeroClass.{u3, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M 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(Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, u2, u1} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)))))) e₂ m))
+ forall {M : Type.{u2}} {N : Type.{u1}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : Module.{u3, u1} R N _inst_1 _inst_5] {ι : Type.{u5}} {κ : Type.{u4}} (e₁ : Equiv.{succ u5, succ u4} ι κ) (e₂ : LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (i : ι) (m : M), Eq.{max (succ u1) (succ u4)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) => Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (Finsupp.single.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) i m)) 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Case conversion may be inaccurate. Consider using '#align finsupp.lcongr_single Finsupp.lcongr_singleₓ'. -/
@[simp]
theorem lcongr_single {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N) (i : ι) (m : M) :
@@ -1499,9 +1499,9 @@ theorem lcongr_single {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N)
/- warning: finsupp.lcongr_apply_apply -> Finsupp.lcongr_apply_apply is a dubious translation:
lean 3 declaration is
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(SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) R M N (SMulZeroClass.toSMul.{u3, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (DistribSMul.toSMulZeroClass.{u3, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (DistribMulAction.toDistribSMul.{u3, u2} R M (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} M _inst_3) (Module.toDistribMulAction.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u3, u1} R N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5)) (DistribSMul.toSMulZeroClass.{u3, u1} R N (AddMonoid.toAddZeroClass.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5)) (DistribMulAction.toDistribSMul.{u3, u1} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_5) (Module.toDistribMulAction.{u3, u1} R N _inst_1 _inst_5 _inst_6)))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) R M N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} M _inst_3) (AddCommMonoid.toAddMonoid.{u1} N _inst_5) (Module.toDistribMulAction.{u3, u2} R M _inst_1 _inst_3 _inst_4) (Module.toDistribMulAction.{u3, u1} R N _inst_1 _inst_5 _inst_6) (SemilinearMapClass.distribMulActionHomClass.{u3, u2, u1, max u2 u1} R M N (LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (SemilinearEquivClass.instSemilinearMapClass.{u3, u3, u2, u1, max u2 u1} R R M N (LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, u2, u1} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)))))) e₂ (FunLike.coe.{max (succ u5) (succ u2), succ u5, succ u2} (Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => M) _x) (Finsupp.funLike.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) f (FunLike.coe.{max (succ u5) (succ u4), succ u4, succ u5} (Equiv.{succ u4, succ u5} κ ι) κ (fun (_x : κ) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : κ) => ι) _x) (Equiv.instFunLikeEquiv.{succ u4, succ u5} κ ι) (Equiv.symm.{succ u5, succ u4} ι κ e₁) k)))
+ forall {M : Type.{u2}} {N : Type.{u1}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : Module.{u3, u1} R N _inst_1 _inst_5] {ι : Type.{u5}} {κ : Type.{u4}} (e₁ : Equiv.{succ u5, succ u4} ι κ) (e₂ : LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (f : Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (k : κ), Eq.{succ u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : κ) => N) k) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) κ (fun (_x : κ) => (fun 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(AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u5, u2} ι M _inst_3) (Finsupp.addCommMonoid.{u4, u1} κ N _inst_5) (Finsupp.module.{u5, u2, u3} ι M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u1, u3} κ N R _inst_1 _inst_5 _inst_6) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)))))) (Finsupp.lcongr.{u2, u1, u3, u5, u4} M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 ι κ e₁ e₂) f) k) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R 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(AddCommMonoid.toAddMonoid.{u1} N _inst_5)) (DistribSMul.toSMulZeroClass.{u3, u1} R N (AddMonoid.toAddZeroClass.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5)) (DistribMulAction.toDistribSMul.{u3, u1} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_5) (Module.toDistribMulAction.{u3, u1} R N _inst_1 _inst_5 _inst_6)))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) R M N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} M _inst_3) (AddCommMonoid.toAddMonoid.{u1} N _inst_5) (Module.toDistribMulAction.{u3, u2} R M _inst_1 _inst_3 _inst_4) 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(Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, u2, u1} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)))))) e₂ (FunLike.coe.{max (succ u5) (succ u2), succ u5, succ u2} (Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => M) _x) (Finsupp.funLike.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) f (FunLike.coe.{max (succ u5) (succ u4), succ u4, succ u5} (Equiv.{succ u4, succ u5} κ ι) κ (fun (_x : κ) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : κ) => ι) _x) (Equiv.instFunLikeEquiv.{succ u4, succ u5} κ ι) (Equiv.symm.{succ u5, succ u4} ι κ e₁) k)))
Case conversion may be inaccurate. Consider using '#align finsupp.lcongr_apply_apply Finsupp.lcongr_apply_applyₓ'. -/
@[simp]
theorem lcongr_apply_apply {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N) (f : ι →₀ M) (k : κ) :
@@ -1513,7 +1513,7 @@ theorem lcongr_apply_apply {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[
lean 3 declaration is
forall {M : Type.{u1}} {N : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : Module.{u3, u2} R N _inst_1 _inst_5] {ι : Type.{u4}} {κ : Type.{u5}} (e₁ : Equiv.{succ u4, succ u5} ι κ) (e₂ : LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (k : κ) (n : N), Eq.{max (succ u4) (succ u1)} (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (coeFn.{max (succ (max u5 u2)) (succ (max u4 u1)), max (succ (max u5 u2)) (succ (max u4 u1))} (LinearEquiv.{u3, u3, max u5 u2, max u4 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.addCommMonoid.{u5, u2} κ N _inst_5) (Finsupp.addCommMonoid.{u4, u1} ι M _inst_3) (Finsupp.module.{u5, u2, u3} κ N R _inst_1 _inst_5 _inst_6) (Finsupp.module.{u4, u1, u3} ι M R _inst_1 _inst_3 _inst_4)) (fun (_x : LinearEquiv.{u3, u3, max u5 u2, max u4 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.addCommMonoid.{u5, u2} κ N _inst_5) (Finsupp.addCommMonoid.{u4, u1} ι M _inst_3) (Finsupp.module.{u5, u2, u3} κ N R _inst_1 _inst_5 _inst_6) (Finsupp.module.{u4, u1, u3} ι M R _inst_1 _inst_3 _inst_4)) => (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) -> (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (LinearEquiv.hasCoeToFun.{u3, u3, max u5 u2, max u4 u1} R R (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u5, u2} κ N _inst_5) (Finsupp.addCommMonoid.{u4, u1} ι M _inst_3) (Finsupp.module.{u5, u2, u3} κ N R _inst_1 _inst_5 _inst_6) (Finsupp.module.{u4, u1, u3} ι M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)) (LinearEquiv.symm.{u3, u3, max u4 u1, max u5 u2} R R (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u1} ι M _inst_3) (Finsupp.addCommMonoid.{u5, u2} κ N _inst_5) (Finsupp.module.{u4, u1, u3} ι M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u5, u2, u3} κ N R _inst_1 _inst_5 _inst_6) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.lcongr.{u1, u2, u3, u4, u5} M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 ι κ e₁ e₂)) (Finsupp.single.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))) k n)) (Finsupp.single.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (coeFn.{max 1 (max (succ u5) (succ u4)) (succ u4) (succ u5), max (succ u5) (succ u4)} (Equiv.{succ u5, succ u4} κ ι) (fun (_x : Equiv.{succ u5, succ u4} κ ι) => κ -> ι) (Equiv.hasCoeToFun.{succ u5, succ u4} κ ι) (Equiv.symm.{succ u4, succ u5} ι κ e₁) k) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) N M _inst_5 _inst_3 _inst_6 _inst_4) (fun (_x : LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) N M _inst_5 _inst_3 _inst_6 _inst_4) => N -> M) (LinearEquiv.hasCoeToFun.{u3, u3, u2, u1} R R N M _inst_1 _inst_1 _inst_5 _inst_3 _inst_6 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)) (LinearEquiv.symm.{u3, u3, u1, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) e₂) n))
but is expected to have type
- forall {M : Type.{u2}} {N : Type.{u1}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : Module.{u3, u1} R N _inst_1 _inst_5] {ι : Type.{u5}} {κ : Type.{u4}} (e₁ : Equiv.{succ u5, succ u4} ι κ) (e₂ : LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (k : κ) (n : N), Eq.{max (succ u2) (succ u5)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) => Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.single.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5)) k n)) 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(AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) => Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _x) (SMulHomClass.toFunLike.{max (max (max u2 u1) u4) u5, u3, max u1 u4, max u2 u5} (LinearEquiv.{u3, u3, max u1 u4, max u2 u5} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u1} κ N _inst_5) (Finsupp.addCommMonoid.{u5, u2} ι M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u1, u3} κ N R _inst_1 _inst_5 _inst_6) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u5, u2, u3} ι M R _inst_1 _inst_3 _inst_4)) R (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulZeroClass.toSMul.{u3, max u1 u4} R (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (AddMonoid.toZero.{max u1 u4} (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (Finsupp.addCommMonoid.{u4, u1} κ N _inst_5))) (DistribSMul.toSMulZeroClass.{u3, max u1 u4} R (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (AddMonoid.toAddZeroClass.{max u1 u4} (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N 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(Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) N M _inst_5 _inst_3 _inst_6 _inst_4) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : N) => M) _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u1, u2} (LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) N M _inst_5 _inst_3 _inst_6 _inst_4) R N M (SMulZeroClass.toSMul.{u3, u1} R N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5)) (DistribSMul.toSMulZeroClass.{u3, u1} R N (AddMonoid.toAddZeroClass.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5)) (DistribMulAction.toDistribSMul.{u3, u1} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_5) (Module.toDistribMulAction.{u3, u1} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u3, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (DistribSMul.toSMulZeroClass.{u3, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (DistribMulAction.toDistribSMul.{u3, u2} R M (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} M _inst_3) (Module.toDistribMulAction.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u1, u2} (LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) N M _inst_5 _inst_3 _inst_6 _inst_4) R N M (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_5) (AddCommMonoid.toAddMonoid.{u2} M _inst_3) (Module.toDistribMulAction.{u3, u1} R N _inst_1 _inst_5 _inst_6) (Module.toDistribMulAction.{u3, u2} R M _inst_1 _inst_3 _inst_4) (SemilinearMapClass.distribMulActionHomClass.{u3, u1, u2, max u2 u1} R N M (LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) N M _inst_5 _inst_3 _inst_6 _inst_4) _inst_1 _inst_5 _inst_3 _inst_6 _inst_4 (SemilinearEquivClass.instSemilinearMapClass.{u3, u3, u1, u2, max u2 u1} R R N M (LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) N M _inst_5 _inst_3 _inst_6 _inst_4) _inst_1 _inst_1 _inst_5 _inst_3 _inst_6 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, u1, u2} R R N M _inst_1 _inst_1 _inst_5 _inst_3 _inst_6 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)))))) (LinearEquiv.symm.{u3, u3, u2, u1} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) e₂) n))
+ forall {M : Type.{u2}} {N : Type.{u1}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : Module.{u3, u1} R N _inst_1 _inst_5] {ι : Type.{u5}} {κ : Type.{u4}} (e₁ : Equiv.{succ u5, succ u4} ι κ) (e₂ : LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6) (k : κ) (n : N), Eq.{max (succ u2) (succ u5)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) => Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.single.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5)) k n)) 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(MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_5) (Module.toDistribMulAction.{u3, u1} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u3, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (DistribSMul.toSMulZeroClass.{u3, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (DistribMulAction.toDistribSMul.{u3, u2} R M (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} M _inst_3) (Module.toDistribMulAction.{u3, u2} R M _inst_1 _inst_3 _inst_4)))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u1, u2} (LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) N M _inst_5 _inst_3 _inst_6 _inst_4) R N M (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_5) (AddCommMonoid.toAddMonoid.{u2} M _inst_3) (Module.toDistribMulAction.{u3, u1} R N _inst_1 _inst_5 _inst_6) (Module.toDistribMulAction.{u3, u2} R M _inst_1 _inst_3 _inst_4) (SemilinearMapClass.distribMulActionHomClass.{u3, u1, u2, max u2 u1} R N M (LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) N M _inst_5 _inst_3 _inst_6 _inst_4) _inst_1 _inst_5 _inst_3 _inst_6 _inst_4 (SemilinearEquivClass.instSemilinearMapClass.{u3, u3, u1, u2, max u2 u1} R R N M (LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) N M _inst_5 _inst_3 _inst_6 _inst_4) _inst_1 _inst_1 _inst_5 _inst_3 _inst_6 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, u1, u2} R R N M _inst_1 _inst_1 _inst_5 _inst_3 _inst_6 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)))))) (LinearEquiv.symm.{u3, u3, u2, u1} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) e₂) n))
Case conversion may be inaccurate. Consider using '#align finsupp.lcongr_symm_single Finsupp.lcongr_symm_singleₓ'. -/
theorem lcongr_symm_single {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N) (k : κ) (n : N) :
(lcongr e₁ e₂).symm (Finsupp.single k n) = Finsupp.single (e₁.symm k) (e₂.symm n) :=
@@ -1526,7 +1526,7 @@ theorem lcongr_symm_single {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[
lean 3 declaration is
forall {M : Type.{u1}} {N : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : Module.{u3, u2} R N _inst_1 _inst_5] {ι : Type.{u4}} {κ : Type.{u5}} (e₁ : Equiv.{succ u4, succ u5} ι κ) (e₂ : LinearEquiv.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6), Eq.{max (succ (max u5 u2)) (succ (max u4 u1))} (LinearEquiv.{u3, u3, max u5 u2, max u4 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.addCommMonoid.{u5, u2} κ N _inst_5) (Finsupp.addCommMonoid.{u4, u1} ι M _inst_3) (Finsupp.module.{u5, u2, u3} κ N R _inst_1 _inst_5 _inst_6) (Finsupp.module.{u4, u1, u3} ι M R _inst_1 _inst_3 _inst_4)) (LinearEquiv.symm.{u3, u3, max u4 u1, max u5 u2} R R (Finsupp.{u4, u1} ι M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u5, u2} κ N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u1} ι M _inst_3) (Finsupp.addCommMonoid.{u5, u2} κ N _inst_5) (Finsupp.module.{u4, u1, u3} ι M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u5, u2, u3} κ N R _inst_1 _inst_5 _inst_6) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.lcongr.{u1, u2, u3, u4, u5} M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 ι κ e₁ e₂)) (Finsupp.lcongr.{u2, u1, u3, u5, u4} N M R _inst_1 _inst_5 _inst_6 _inst_3 _inst_4 κ ι (Equiv.symm.{succ u4, succ u5} ι κ e₁) (LinearEquiv.symm.{u3, u3, u1, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) e₂))
but is expected to have type
- forall {M : Type.{u2}} {N : Type.{u1}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : Module.{u3, u1} R N _inst_1 _inst_5] {ι : Type.{u5}} {κ : Type.{u4}} (e₁ : Equiv.{succ u5, succ u4} ι κ) (e₂ : LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6), Eq.{max (max (max (succ u2) (succ u1)) (succ u4)) (succ u5)} (LinearEquiv.{u3, u3, max u1 u4, max u2 u5} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u1} κ N _inst_5) (Finsupp.addCommMonoid.{u5, u2} ι M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u1, u3} κ N R _inst_1 _inst_5 _inst_6) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u5, u2, u3} ι M R _inst_1 _inst_3 _inst_4)) (LinearEquiv.symm.{u3, u3, max u2 u5, max u1 u4} R R (Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u5, u2} ι M _inst_3) (Finsupp.addCommMonoid.{u4, u1} κ N _inst_5) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u5, u2, u3} ι M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u1, u3} κ N R _inst_1 _inst_5 _inst_6) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.lcongr.{u2, u1, u3, u5, u4} M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 ι κ e₁ e₂)) (Finsupp.lcongr.{u1, u2, u3, u4, u5} N M R _inst_1 _inst_5 _inst_6 _inst_3 _inst_4 κ ι (Equiv.symm.{succ u5, succ u4} ι κ e₁) (LinearEquiv.symm.{u3, u3, u2, u1} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) e₂))
+ forall {M : Type.{u2}} {N : Type.{u1}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : Module.{u3, u1} R N _inst_1 _inst_5] {ι : Type.{u5}} {κ : Type.{u4}} (e₁ : Equiv.{succ u5, succ u4} ι κ) (e₂ : LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M N _inst_3 _inst_5 _inst_4 _inst_6), Eq.{max (max (max (succ u2) (succ u1)) (succ u4)) (succ u5)} (LinearEquiv.{u3, u3, max u1 u4, max u2 u5} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) (Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u1} κ N _inst_5) (Finsupp.addCommMonoid.{u5, u2} ι M _inst_3) (Finsupp.module.{u4, u1, u3} κ N R _inst_1 _inst_5 _inst_6) (Finsupp.module.{u5, u2, u3} ι M R _inst_1 _inst_3 _inst_4)) (LinearEquiv.symm.{u3, u3, max u2 u5, max u1 u4} R R (Finsupp.{u5, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u4, u1} κ N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_5))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u5, u2} ι M _inst_3) (Finsupp.addCommMonoid.{u4, u1} κ N _inst_5) (Finsupp.module.{u5, u2, u3} ι M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u1, u3} κ N R _inst_1 _inst_5 _inst_6) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.lcongr.{u2, u1, u3, u5, u4} M N R _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 ι κ e₁ e₂)) (Finsupp.lcongr.{u1, u2, u3, u4, u5} N M R _inst_1 _inst_5 _inst_6 _inst_3 _inst_4 κ ι (Equiv.symm.{succ u5, succ u4} ι κ e₁) (LinearEquiv.symm.{u3, u3, u2, u1} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) e₂))
Case conversion may be inaccurate. Consider using '#align finsupp.lcongr_symm Finsupp.lcongr_symmₓ'. -/
@[simp]
theorem lcongr_symm {ι κ : Sort _} (e₁ : ι ≃ κ) (e₂ : M ≃ₗ[R] N) :
@@ -1544,7 +1544,7 @@ variable (R)
lean 3 declaration is
forall {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {α : Type.{u3}} {β : Type.{u4}}, LinearEquiv.{u2, u2, max (max u3 u4) u1, max (max u3 u1) u4 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (Finsupp.{max u3 u4, u1} (Sum.{u3, u4} α β) M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Prod.{max u3 u1, max u4 u1} (Finsupp.{u3, u1} α M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u4, u1} β M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (Finsupp.addCommMonoid.{max u3 u4, u1} (Sum.{u3, u4} α β) M _inst_3) (Prod.addCommMonoid.{max u3 u1, max u4 u1} (Finsupp.{u3, u1} α M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u4, u1} β M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.addCommMonoid.{u3, u1} α M _inst_3) (Finsupp.addCommMonoid.{u4, u1} β M _inst_3)) (Finsupp.module.{max u3 u4, u1, u2} (Sum.{u3, u4} α β) M R _inst_1 _inst_3 _inst_4) (Prod.module.{u2, max u3 u1, max u4 u1} R (Finsupp.{u3, u1} α M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.{u4, u1} β M (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α M _inst_3) (Finsupp.addCommMonoid.{u4, u1} β M _inst_3) (Finsupp.module.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u4, u1, u2} β M R _inst_1 _inst_3 _inst_4))
but is expected to have type
- forall {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {α : Type.{u3}} {β : Type.{u4}}, LinearEquiv.{u2, u2, max u1 u4 u3, max (max u1 u4) u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (Finsupp.{max u4 u3, u1} (Sum.{u3, u4} α β) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Prod.{max u1 u3, max u1 u4} (Finsupp.{u3, u1} α M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Finsupp.{u4, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Finsupp.addCommMonoid.{max u3 u4, u1} (Sum.{u3, u4} α β) M _inst_3) (Prod.instAddCommMonoidSum.{max u1 u3, max u1 u4} (Finsupp.{u3, u1} α M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Finsupp.{u4, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Finsupp.addCommMonoid.{u3, u1} α M _inst_3) (Finsupp.addCommMonoid.{u4, u1} β M _inst_3)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{max u3 u4, u1, u2} (Sum.{u3, u4} α β) M R _inst_1 _inst_3 _inst_4) (Prod.module.{u2, max u1 u3, max u1 u4} R (Finsupp.{u3, u1} α M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Finsupp.{u4, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α M _inst_3) (Finsupp.addCommMonoid.{u4, u1} β M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u1, u2} β M R _inst_1 _inst_3 _inst_4))
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Case conversion may be inaccurate. Consider using '#align finsupp.sum_finsupp_lequiv_prod_finsupp Finsupp.sumFinsuppLEquivProdFinsuppₓ'. -/
/-- The linear equivalence between `(α ⊕ β) →₀ M` and `(α →₀ M) × (β →₀ M)`.
@@ -1562,9 +1562,9 @@ def sumFinsuppLEquivProdFinsupp {α β : Type _} : (Sum α β →₀ M) ≃ₗ[R
/- warning: finsupp.fst_sum_finsupp_lequiv_prod_finsupp -> Finsupp.fst_sumFinsuppLEquivProdFinsupp is a dubious translation:
lean 3 declaration is
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but is expected to have type
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+ forall {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {α : Type.{u4}} {β : Type.{u3}} (f : Finsupp.{max u3 u4, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (x : α), Eq.{succ u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) x) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) α (fun (_x : α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) _x) (Finsupp.funLike.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Prod.fst.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (max (succ 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Case conversion may be inaccurate. Consider using '#align finsupp.fst_sum_finsupp_lequiv_prod_finsupp Finsupp.fst_sumFinsuppLEquivProdFinsuppₓ'. -/
theorem fst_sumFinsuppLEquivProdFinsupp {α β : Type _} (f : Sum α β →₀ M) (x : α) :
(sumFinsuppLEquivProdFinsupp R f).1 x = f (Sum.inl x) :=
@@ -1573,9 +1573,9 @@ theorem fst_sumFinsuppLEquivProdFinsupp {α β : Type _} (f : Sum α β →₀ M
/- warning: finsupp.snd_sum_finsupp_lequiv_prod_finsupp -> Finsupp.snd_sumFinsuppLEquivProdFinsupp is a dubious translation:
lean 3 declaration is
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but is expected to have type
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+ forall {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {α : Type.{u4}} {β : Type.{u3}} (f : Finsupp.{max u3 u4, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (y : β), Eq.{succ u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : β) => M) y) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) β (fun (_x : β) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : β) => M) _x) (Finsupp.funLike.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Prod.snd.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (max (succ 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Case conversion may be inaccurate. Consider using '#align finsupp.snd_sum_finsupp_lequiv_prod_finsupp Finsupp.snd_sumFinsuppLEquivProdFinsuppₓ'. -/
theorem snd_sumFinsuppLEquivProdFinsupp {α β : Type _} (f : Sum α β →₀ M) (y : β) :
(sumFinsuppLEquivProdFinsupp R f).2 y = f (Sum.inr y) :=
@@ -1584,9 +1584,9 @@ theorem snd_sumFinsuppLEquivProdFinsupp {α β : Type _} (f : Sum α β →₀ M
/- warning: finsupp.sum_finsupp_lequiv_prod_finsupp_symm_inl -> Finsupp.sumFinsuppLEquivProdFinsupp_symm_inl is a dubious translation:
lean 3 declaration is
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but is expected to have type
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R (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Prod.instAddCommMonoidSum.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} β M _inst_3))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} R (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M 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_inst_1 _inst_3 _inst_4)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} R (Finsupp.{max u3 u4, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (AddMonoid.toZero.{max (max u3 u4) u2} (Finsupp.{max u3 u4, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (Finsupp.{max u3 u4, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{max u4 u3, u2} (Sum.{u4, u3} α β) M _inst_3))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} R (Finsupp.{max u3 u4, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (Finsupp.{max u3 u4, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (Finsupp.{max u3 u4, u2} 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_inst_1 _inst_3 _inst_4))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{max u3 u4, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Prod.instAddCommMonoidSum.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} β M _inst_3)) (Finsupp.addCommMonoid.{max u4 u3, u2} (Sum.{u4, u3} α β) M _inst_3) (Prod.module.{u1, max u2 u4, max u2 u3} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} β M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} β M R _inst_1 _inst_3 _inst_4)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{max u4 u3, u2, u1} (Sum.{u4, u3} α β) M R _inst_1 _inst_3 _inst_4)) R (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{max u3 u4, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Prod.instAddCommMonoidSum.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} β M _inst_3))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (Finsupp.{max u3 u4, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{max u4 u3, u2} (Sum.{u4, u3} α β) M _inst_3)) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} R (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Prod.instAddCommMonoidSum.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} β M _inst_3)) (Prod.module.{u1, max u2 u4, max u2 u3} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} β M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} β M R _inst_1 _inst_3 _inst_4))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} R (Finsupp.{max u3 u4, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{max u4 u3, u2} (Sum.{u4, u3} α β) M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{max u4 u3, u2, u1} (Sum.{u4, u3} α β) M R _inst_1 _inst_3 _inst_4)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} R (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{max u3 u4, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M 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u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Prod.instAddCommMonoidSum.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} β M _inst_3)))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} R (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Prod.instAddCommMonoidSum.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} β M _inst_3))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} R (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Prod.instAddCommMonoidSum.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M 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(AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (Finsupp.{max u3 u4, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{max u4 u3, u2} (Sum.{u4, u3} α β) M _inst_3)) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} R (Finsupp.{max u3 u4, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{max u4 u3, u2} (Sum.{u4, u3} α β) M _inst_3) (Finsupp.module.{max u4 u3, u2, u1} (Sum.{u4, u3} α β) M R _inst_1 _inst_3 _inst_4))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{max u3 u4, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Prod.instAddCommMonoidSum.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} β M _inst_3)) (Finsupp.addCommMonoid.{max u4 u3, u2} (Sum.{u4, u3} α β) M _inst_3) (Prod.module.{u1, max u2 u4, max u2 u3} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} β M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} β M R _inst_1 _inst_3 _inst_4)) (Finsupp.module.{max u4 u3, u2, u1} (Sum.{u4, u3} α β) M R _inst_1 _inst_3 _inst_4)) R (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Finsupp.{max u3 u4, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Prod.instAddCommMonoidSum.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} β M _inst_3))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (Finsupp.{max u3 u4, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{max u4 u3, u2} (Sum.{u4, u3} α β) M _inst_3)) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} R (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Prod.instAddCommMonoidSum.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M 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Case conversion may be inaccurate. Consider using '#align finsupp.sum_finsupp_lequiv_prod_finsupp_symm_inl Finsupp.sumFinsuppLEquivProdFinsupp_symm_inlₓ'. -/
theorem sumFinsuppLEquivProdFinsupp_symm_inl {α β : Type _} (fg : (α →₀ M) × (β →₀ M)) (x : α) :
((sumFinsuppLEquivProdFinsupp R).symm fg) (Sum.inl x) = fg.1 x :=
@@ -1595,9 +1595,9 @@ theorem sumFinsuppLEquivProdFinsupp_symm_inl {α β : Type _} (fg : (α →₀ M
/- warning: finsupp.sum_finsupp_lequiv_prod_finsupp_symm_inr -> Finsupp.sumFinsuppLEquivProdFinsupp_symm_inr is a dubious translation:
lean 3 declaration is
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but is expected to have type
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(AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} β M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} β M R _inst_1 _inst_3 _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.sumFinsuppLEquivProdFinsupp.{u2, u1, u4, u3} M R _inst_1 _inst_3 _inst_4 α β)) fg) (Sum.inr.{u4, u3} α β y)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) β (fun (_x : β) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : β) => M) _x) (Finsupp.funLike.{u3, u2} β M (AddMonoid.toZero.{u2} M 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+ forall {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {α : Type.{u4}} {β : Type.{u3}} (fg : Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (y : β), Eq.{succ u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Sum.{u4, u3} α β) => M) (Sum.inr.{u4, u3} α β y)) (FunLike.coe.{max (succ (max u4 u3)) (succ u2), succ (max u4 u3), succ u2} (Finsupp.{max u4 u3, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Sum.{u4, u3} α β) (fun (_x : Sum.{u4, u3} α β) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Sum.{u4, u3} α β) => M) _x) (Finsupp.funLike.{max u4 u3, u2} (Sum.{u4, u3} α β) M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (FunLike.coe.{max (max (succ u3) 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(Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) (Prod.instAddCommMonoidSum.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} β M _inst_3))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} R (Prod.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Prod.instAddCommMonoidSum.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M 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M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{max u4 u3, u2} (Sum.{u4, u3} α β) M _inst_3) (Prod.instAddCommMonoidSum.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} β M _inst_3)) (Finsupp.module.{max u4 u3, u2, u1} (Sum.{u4, u3} α β) M R _inst_1 _inst_3 _inst_4) (Prod.module.{u1, max u2 u4, max u2 u3} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} β M _inst_3) (Finsupp.module.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.module.{u3, u2, u1} β M R _inst_1 _inst_3 _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.sumFinsuppLEquivProdFinsupp.{u2, u1, u4, u3} M R _inst_1 _inst_3 _inst_4 α β)) fg) (Sum.inr.{u4, u3} α β y)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) β (fun (_x : β) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : β) => M) _x) (Finsupp.funLike.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Prod.snd.{max u2 u4, max u2 u3} (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} β M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) fg) y)
Case conversion may be inaccurate. Consider using '#align finsupp.sum_finsupp_lequiv_prod_finsupp_symm_inr Finsupp.sumFinsuppLEquivProdFinsupp_symm_inrₓ'. -/
theorem sumFinsuppLEquivProdFinsupp_symm_inr {α β : Type _} (fg : (α →₀ M) × (β →₀ M)) (y : β) :
((sumFinsuppLEquivProdFinsupp R).symm fg) (Sum.inr y) = fg.2 y :=
@@ -1616,7 +1616,7 @@ variable (R)
lean 3 declaration is
forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] {η : Type.{u2}} [_inst_9 : Fintype.{u2} η] {M : Type.{u3}} {ιs : η -> Type.{u4}} [_inst_11 : AddCommMonoid.{u3} M] [_inst_12 : Module.{u1, u3} R M _inst_1 _inst_11], LinearEquiv.{u1, u1, max (max u2 u4) u3, max u2 u4 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{max u2 u4, u3} (Sigma.{u2, u4} η (fun (j : η) => ιs j)) M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_11)))) (forall (j : η), Finsupp.{u4, u3} (ιs j) M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_11)))) (Finsupp.addCommMonoid.{max u2 u4, u3} (Sigma.{u2, u4} η (fun (j : η) => ιs j)) M _inst_11) (Pi.addCommMonoid.{u2, max u4 u3} η (fun (j : η) => Finsupp.{u4, u3} (ιs j) M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_11)))) (fun (i : η) => Finsupp.addCommMonoid.{u4, u3} (ιs i) M _inst_11)) (Finsupp.module.{max u2 u4, u3, u1} (Sigma.{u2, u4} η (fun (j : η) => ιs j)) M R _inst_1 _inst_11 _inst_12) (Pi.module.{u2, max u4 u3, u1} η (fun (j : η) => Finsupp.{u4, u3} (ιs j) M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_11)))) R _inst_1 (fun (i : η) => Finsupp.addCommMonoid.{u4, u3} (ιs i) M _inst_11) (fun (i : η) => Finsupp.module.{u4, u3, u1} (ιs i) M R _inst_1 _inst_11 _inst_12))
but is expected to have type
- forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] {η : Type.{u2}} [_inst_9 : Fintype.{u2} η] {M : Type.{u3}} {ιs : η -> Type.{u4}} [_inst_11 : AddCommMonoid.{u3} M] [_inst_12 : Module.{u1, u3} R M _inst_1 _inst_11], LinearEquiv.{u1, u1, max u3 u4 u2, max (max u2 u3) u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{max u4 u2, u3} (Sigma.{u2, u4} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_11))) (forall (j : η), Finsupp.{u4, u3} (ιs j) M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_11))) (Finsupp.addCommMonoid.{max u2 u4, u3} (Sigma.{u2, u4} η (fun (j : η) => ιs j)) M _inst_11) (Pi.addCommMonoid.{u2, max u3 u4} η (fun (j : η) => Finsupp.{u4, u3} (ιs j) M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_11))) (fun (i : η) => Finsupp.addCommMonoid.{u4, u3} (ιs i) M _inst_11)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{max u2 u4, u3, u1} (Sigma.{u2, u4} η (fun (j : η) => ιs j)) M R _inst_1 _inst_11 _inst_12) (Pi.module.{u2, max u3 u4, u1} η (fun (j : η) => Finsupp.{u4, u3} (ιs j) M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_11))) R _inst_1 (fun (i : η) => Finsupp.addCommMonoid.{u4, u3} (ιs i) M _inst_11) (fun (i : η) => Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u3, u1} (ιs i) M R _inst_1 _inst_11 _inst_12))
+ forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] {η : Type.{u2}} [_inst_9 : Fintype.{u2} η] {M : Type.{u3}} {ιs : η -> Type.{u4}} [_inst_11 : AddCommMonoid.{u3} M] [_inst_12 : Module.{u1, u3} R M _inst_1 _inst_11], LinearEquiv.{u1, u1, max u3 u4 u2, max (max u2 u3) u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Finsupp.{max u4 u2, u3} (Sigma.{u2, u4} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_11))) (forall (j : η), Finsupp.{u4, u3} (ιs j) M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_11))) (Finsupp.addCommMonoid.{max u2 u4, u3} (Sigma.{u2, u4} η (fun (j : η) => ιs j)) M _inst_11) (Pi.addCommMonoid.{u2, max u3 u4} η (fun (j : η) => Finsupp.{u4, u3} (ιs j) M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_11))) (fun (i : η) => Finsupp.addCommMonoid.{u4, u3} (ιs i) M _inst_11)) (Finsupp.module.{max u2 u4, u3, u1} (Sigma.{u2, u4} η (fun (j : η) => ιs j)) M R _inst_1 _inst_11 _inst_12) (Pi.module.{u2, max u3 u4, u1} η (fun (j : η) => Finsupp.{u4, u3} (ιs j) M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_11))) R _inst_1 (fun (i : η) => Finsupp.addCommMonoid.{u4, u3} (ιs i) M _inst_11) (fun (i : η) => Finsupp.module.{u4, u3, u1} (ιs i) M R _inst_1 _inst_11 _inst_12))
Case conversion may be inaccurate. Consider using '#align finsupp.sigma_finsupp_lequiv_pi_finsupp Finsupp.sigmaFinsuppLEquivPiFinsuppₓ'. -/
/-- On a `fintype η`, `finsupp.split` is a linear equivalence between
`(Σ (j : η), ιs j) →₀ M` and `Π j, (ιs j →₀ M)`.
@@ -1632,9 +1632,9 @@ noncomputable def sigmaFinsuppLEquivPiFinsupp {M : Type _} {ιs : η → Type _}
/- warning: finsupp.sigma_finsupp_lequiv_pi_finsupp_apply -> Finsupp.sigmaFinsuppLEquivPiFinsupp_apply is a dubious translation:
lean 3 declaration is
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but is expected to have type
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+ forall (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] {η : Type.{u1}} [_inst_9 : Fintype.{u1} η] {M : Type.{u4}} {ιs : η -> Type.{u3}} [_inst_11 : AddCommMonoid.{u4} M] [_inst_12 : Module.{u2, u4} R M _inst_1 _inst_11] (f : Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (j : η) (i : ιs j), Eq.{succ u4} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ιs j) => M) i) (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (ιs j) (fun (_x : ιs j) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ιs j) => M) _x) (Finsupp.funLike.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u1), max (max (succ u3) (succ u4)) (succ u1), max (max (succ u3) (succ u4)) (succ u1)} (LinearEquiv.{u2, u2, max u4 u3 u1, max (max u1 u4) 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_inst_1 (fun (i : η) => Finsupp.addCommMonoid.{u3, u4} (ιs i) M _inst_11) (fun (i : η) => Finsupp.module.{u3, u4, u2} (ιs i) M R _inst_1 _inst_11 _inst_12))) R (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (forall (j : η), Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (SMulZeroClass.toSMul.{u2, max (max u3 u4) u1} R (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (AddMonoid.toZero.{max (max u3 u4) u1} (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u1} (Finsupp.{max u3 u1, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (Finsupp.addCommMonoid.{max u1 u3, 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Case conversion may be inaccurate. Consider using '#align finsupp.sigma_finsupp_lequiv_pi_finsupp_apply Finsupp.sigmaFinsuppLEquivPiFinsupp_applyₓ'. -/
@[simp]
theorem sigmaFinsuppLEquivPiFinsupp_apply {M : Type _} {ιs : η → Type _} [AddCommMonoid M]
@@ -1644,9 +1644,9 @@ theorem sigmaFinsuppLEquivPiFinsupp_apply {M : Type _} {ιs : η → Type _} [Ad
/- warning: finsupp.sigma_finsupp_lequiv_pi_finsupp_symm_apply -> Finsupp.sigmaFinsuppLEquivPiFinsupp_symm_apply is a dubious translation:
lean 3 declaration is
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+ forall (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] {η : Type.{u1}} [_inst_9 : Fintype.{u1} η] {M : Type.{u4}} {ιs : η -> Type.{u3}} [_inst_11 : AddCommMonoid.{u4} M] [_inst_12 : Module.{u2, u4} R M _inst_1 _inst_11] (f : forall (j : η), Finsupp.{u3, u4} (ιs j) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (ji : Sigma.{u1, u3} η (fun (j : η) => ιs j)), Eq.{succ u4} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Sigma.{u1, u3} η (fun (j : η) => ιs j)) => M) ji) (FunLike.coe.{max (succ (max u1 u3)) (succ u4), succ (max u1 u3), succ u4} (Finsupp.{max u1 u3, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_11))) (Sigma.{u1, u3} η (fun (j : η) => ιs j)) (fun (_x : Sigma.{u1, u3} η (fun (j : η) => ιs j)) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Sigma.{u1, u3} η (fun (j : η) => ιs j)) => M) _x) (Finsupp.funLike.{max u1 u3, u4} (Sigma.{u1, u3} η (fun (j : η) => ιs j)) M (AddMonoid.toZero.{u4} 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Case conversion may be inaccurate. Consider using '#align finsupp.sigma_finsupp_lequiv_pi_finsupp_symm_apply Finsupp.sigmaFinsuppLEquivPiFinsupp_symm_applyₓ'. -/
@[simp]
theorem sigmaFinsuppLEquivPiFinsupp_symm_apply {M : Type _} {ιs : η → Type _} [AddCommMonoid M]
@@ -1661,9 +1661,9 @@ section Prod
/- warning: finsupp.finsupp_prod_lequiv -> Finsupp.finsuppProdLEquiv is a dubious translation:
lean 3 declaration is
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+ forall {α : Type.{u1}} {β : Type.{u2}} (R : Type.{u3}) {M : Type.{u4}} [_inst_9 : Semiring.{u3} R] [_inst_10 : AddCommMonoid.{u4} M] [_inst_11 : Module.{u3, u4} R M _inst_9 _inst_10], LinearEquiv.{u3, u3, max (max u1 u2) u4, max u1 u2 u4} R R _inst_9 _inst_9 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_9)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_9)) (RingHomInvPair.ids.{u3} R _inst_9) (RingHomInvPair.ids.{u3} R _inst_9) (Finsupp.{max u1 u2, u4} (Prod.{u1, u2} α β) M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_10)))) (Finsupp.{u1, max u2 u4} α (Finsupp.{u2, u4} β M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_10)))) (Finsupp.zero.{u2, u4} β M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_10))))) (Finsupp.addCommMonoid.{max u1 u2, u4} (Prod.{u1, u2} α β) M _inst_10) (Finsupp.addCommMonoid.{u1, max u2 u4} α (Finsupp.{u2, u4} β M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_10)))) (Finsupp.addCommMonoid.{u2, u4} β M _inst_10)) (Finsupp.module.{max u1 u2, u4, u3} (Prod.{u1, u2} α β) M R _inst_9 _inst_10 _inst_11) (Finsupp.module.{u1, max u2 u4, u3} α (Finsupp.{u2, u4} β M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_10)))) R _inst_9 (Finsupp.addCommMonoid.{u2, u4} β M _inst_10) (Finsupp.module.{u2, u4, u3} β M R _inst_9 _inst_10 _inst_11))
but is expected to have type
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+ forall {α : Type.{u1}} {β : Type.{u2}} (R : Type.{u3}) {M : Type.{u4}} [_inst_9 : Semiring.{u3} R] [_inst_10 : AddCommMonoid.{u4} M] [_inst_11 : Module.{u3, u4} R M _inst_9 _inst_10], LinearEquiv.{u3, u3, max u4 u2 u1, max (max u4 u2) u1} R R _inst_9 _inst_9 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_9)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_9)) (RingHomInvPair.ids.{u3} R _inst_9) (RingHomInvPair.ids.{u3} R _inst_9) (Finsupp.{max u2 u1, u4} (Prod.{u1, u2} α β) M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_10))) (Finsupp.{u1, max u4 u2} α (Finsupp.{u2, u4} β M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_10))) (Finsupp.zero.{u2, u4} β M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_10)))) (Finsupp.addCommMonoid.{max u1 u2, u4} (Prod.{u1, u2} α β) M _inst_10) (Finsupp.addCommMonoid.{u1, max u2 u4} α (Finsupp.{u2, u4} β M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_10))) (Finsupp.addCommMonoid.{u2, u4} β M _inst_10)) (Finsupp.module.{max u1 u2, u4, u3} (Prod.{u1, u2} α β) M R _inst_9 _inst_10 _inst_11) (Finsupp.module.{u1, max u2 u4, u3} α (Finsupp.{u2, u4} β M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_10))) R _inst_9 (Finsupp.addCommMonoid.{u2, u4} β M _inst_10) (Finsupp.module.{u2, u4, u3} β M R _inst_9 _inst_10 _inst_11))
Case conversion may be inaccurate. Consider using '#align finsupp.finsupp_prod_lequiv Finsupp.finsuppProdLEquivₓ'. -/
/-- The linear equivalence between `α × β →₀ M` and `α →₀ β →₀ M`.
@@ -1682,9 +1682,9 @@ noncomputable def finsuppProdLEquiv {α β : Type _} (R : Type _) {M : Type _} [
/- warning: finsupp.finsupp_prod_lequiv_apply -> Finsupp.finsuppProdLEquiv_apply is a dubious translation:
lean 3 declaration is
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+ forall {α : Type.{u4}} {β : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_9 : Semiring.{u2} R] [_inst_10 : AddCommMonoid.{u1} M] [_inst_11 : Module.{u2, u1} R M _inst_9 _inst_10] (f : Finsupp.{max u3 u4, u1} (Prod.{u4, u3} α β) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (x : α) (y : β), Eq.{succ u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : β) => M) y) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) β (fun (_x : β) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : β) => M) _x) (Finsupp.funLike.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (FunLike.coe.{max (succ u4) (succ (max u3 u1)), succ u4, succ (max u3 u1)} (Finsupp.{u4, max u3 u1} α (Finsupp.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (Finsupp.zero.{u3, u1} β M (AddMonoid.toZero.{u1} M 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Case conversion may be inaccurate. Consider using '#align finsupp.finsupp_prod_lequiv_apply Finsupp.finsuppProdLEquiv_applyₓ'. -/
@[simp]
theorem finsuppProdLEquiv_apply {α β R M : Type _} [Semiring R] [AddCommMonoid M] [Module R M]
@@ -1694,9 +1694,9 @@ theorem finsuppProdLEquiv_apply {α β R M : Type _} [Semiring R] [AddCommMonoid
/- warning: finsupp.finsupp_prod_lequiv_symm_apply -> Finsupp.finsuppProdLEquiv_symm_apply is a dubious translation:
lean 3 declaration is
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but is expected to have type
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(Module.toDistribMulAction.{u2, max (max u1 u3) u4} R (Finsupp.{max u3 u4, u1} (Prod.{u4, u3} α β) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) _inst_9 (Finsupp.addCommMonoid.{max u4 u3, u1} (Prod.{u4, u3} α β) M _inst_10) (Finsupp.module.{max u4 u3, u1, u2} (Prod.{u4, u3} α β) M R _inst_9 _inst_10 _inst_11))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u3) u4, u2, max (max u1 u3) u4, max (max u1 u3) u4} (LinearEquiv.{u2, u2, max (max u1 u3) u4, max (max u1 u3) u4} R R _inst_9 _inst_9 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_9)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_9)) (RingHomInvPair.ids.{u2} R _inst_9) (RingHomInvPair.ids.{u2} R _inst_9) (Finsupp.{u4, max u1 u3} α (Finsupp.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (Finsupp.zero.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10)))) (Finsupp.{max u3 u4, u1} (Prod.{u4, u3} α β) M 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(MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_9)) (AddCommMonoid.toAddMonoid.{max (max u1 u3) u4} (Finsupp.{u4, max u1 u3} α (Finsupp.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (Finsupp.zero.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10)))) (Finsupp.addCommMonoid.{u4, max u3 u1} α (Finsupp.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (Finsupp.addCommMonoid.{u3, u1} β M _inst_10))) (AddCommMonoid.toAddMonoid.{max (max u1 u3) u4} (Finsupp.{max u3 u4, u1} (Prod.{u4, u3} α β) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (Finsupp.addCommMonoid.{max u4 u3, u1} (Prod.{u4, u3} α β) M _inst_10)) (Module.toDistribMulAction.{u2, max (max u1 u3) u4} R (Finsupp.{u4, max u1 u3} α (Finsupp.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (Finsupp.zero.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10)))) _inst_9 (Finsupp.addCommMonoid.{u4, max u3 u1} α (Finsupp.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) (Finsupp.addCommMonoid.{u3, u1} β M _inst_10)) (Finsupp.module.{u4, max u3 u1, u2} α (Finsupp.{u3, u1} β M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) R _inst_9 (Finsupp.addCommMonoid.{u3, u1} β M _inst_10) (Finsupp.module.{u3, u1, u2} β M R _inst_9 _inst_10 _inst_11))) (Module.toDistribMulAction.{u2, max (max u1 u3) u4} R (Finsupp.{max u3 u4, u1} (Prod.{u4, u3} α β) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_10))) _inst_9 (Finsupp.addCommMonoid.{max u4 u3, u1} (Prod.{u4, u3} α β) M _inst_10) (Finsupp.module.{max u4 u3, u1, u2} (Prod.{u4, u3} α β) M R _inst_9 _inst_10 _inst_11)) (SemilinearMapClass.distribMulActionHomClass.{u2, max (max u1 u3) u4, max (max u1 u3) u4, max (max u1 u3) u4} R (Finsupp.{u4, max u1 u3} α (Finsupp.{u3, u1} β M 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Case conversion may be inaccurate. Consider using '#align finsupp.finsupp_prod_lequiv_symm_apply Finsupp.finsuppProdLEquiv_symm_applyₓ'. -/
@[simp]
theorem finsuppProdLEquiv_symm_apply {α β R M : Type _} [Semiring R] [AddCommMonoid M] [Module R M]
@@ -1775,7 +1775,7 @@ variable (S)
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] (S : Type.{u4}) [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (x : α -> R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R 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(Semiring.toNonAssocSemiring.{u3} R _inst_2))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))) M _inst_2 _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Finsupp.total.{u1, u2, u3} α M R _inst_2 _inst_3 _inst_4 v) (coeFn.{succ (max u1 u3), succ (max u1 u3)} (LinearEquiv.{u3, u3, max u1 u3, max u1 u3} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHomInvPair.ids.{u3} R _inst_2) (RingHomInvPair.ids.{u3} R _inst_2) (α -> R) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R 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(Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) x)
but is expected to have type
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(MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (x : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) => M) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R 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u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (α -> R) (fun (a : α -> R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> R) => Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) a) (SMulHomClass.toFunLike.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (α -> R) (AddMonoid.toZero.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (α -> R) (AddMonoid.toAddZeroClass.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (α -> R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u3 u2, max u3 u2, max u3 u2} R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u3 u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} 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(Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 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(a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u3 u2, max u3 u2, max u3 u2} R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun 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NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u3, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13965 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13965 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13965 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) x)
+ forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (x : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) => M) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (α -> R) (fun (a : α -> R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> R) => Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) a) (SMulHomClass.toFunLike.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (α -> R) (AddMonoid.toZero.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (α -> R) (AddMonoid.toAddZeroClass.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (α -> R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u3 u2, max u3 u2, max u3 u2} R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u3 u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α 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(AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 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R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.module.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u3 u2, max u3 u2, max u3 u2} R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.module.{u3, u2, u2} 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Case conversion may be inaccurate. Consider using '#align finsupp.total_eq_fintype_total_apply Finsupp.total_eq_fintype_total_applyₓ'. -/
theorem Finsupp.total_eq_fintype_total_apply (x : α → R) :
Finsupp.total α M R v ((Finsupp.linearEquivFunOnFinite R R α).symm x) = Fintype.total R S v x :=
@@ -1791,7 +1791,7 @@ theorem Finsupp.total_eq_fintype_total_apply (x : α → R) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] (S : Type.{u4}) [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (LinearMap.comp.{u3, u3, u3, max u1 u3, max u1 u3, u2} R R R (α -> R) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))) M _inst_2 _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHomCompTriple.right_ids.{u3, u3} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Finsupp.total.{u1, u2, u3} α M R _inst_2 _inst_3 _inst_4 v) (LinearEquiv.toLinearMap.{u3, u3, max u1 u3, max u1 u3} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHomInvPair.ids.{u3} R _inst_2) (RingHomInvPair.ids.{u3} R _inst_2) (α -> R) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))))) (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) (LinearEquiv.symm.{u3, u3, max u1 u3, max u1 u3} R R (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))))) (α -> R) _inst_2 _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHomInvPair.ids.{u3} R _inst_2) (RingHomInvPair.ids.{u3} R _inst_2) (Finsupp.linearEquivFunOnFinite.{u3, u3, u1} R R α (Finite.of_fintype.{u1} α _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) _inst_2 (Semiring.toModule.{u3} R _inst_2))))) (coeFn.{max (succ (max u1 u2)) (succ (max (max u1 u3) u2)), max (succ (max u1 u2)) (succ (max (max u1 u3) u2))} (LinearMap.{u4, u4, max u1 u2, max (max u1 u3) u2} S S _inst_5 _inst_5 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4)) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, max (max u1 u3) u2} S S (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)
but is expected to have type
- forall {α : Type.{u4}} {M : Type.{u3}} (R : Type.{u2}) [_inst_1 : Fintype.{u4} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u3} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u3} R S M (SMulZeroClass.toSMul.{u2, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u2, u3} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u3} S M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u1, u3} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (LinearMap.comp.{u2, u2, u2, max u4 u2, max u4 u2, u3} R R R (α -> R) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) M _inst_2 _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomCompTriple.ids.{u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Finsupp.total.{u4, u3, u2} α M R _inst_2 _inst_3 _inst_4 v) (LinearEquiv.toLinearMap.{u2, u2, max u4 u2, max u4 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u4, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (LinearEquiv.symm.{u2, u2, max u4 u2, max u4 u2} R R (Finsupp.{u4, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (α -> R) _inst_2 _inst_2 (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (Finsupp.linearEquivFunOnFinite.{u2, u2, u4} R R α (Finite.of_fintype.{u4} α _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) _inst_2 (Semiring.toModule.{u2} R _inst_2))))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), max (max (succ u2) (succ u3)) (succ u4)} (LinearMap.{u1, u1, max u4 u3, max u3 u4 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u4, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13965 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u4 u2, u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u4, u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13965 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u4 u2, u3} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u4, max (max u2 u3) u4} S S (α -> M) (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u4, u3} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u4 u2, u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u4, u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13965 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u4 u2, u3} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u4, u3, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)
+ forall {α : Type.{u4}} {M : Type.{u3}} (R : Type.{u2}) [_inst_1 : Fintype.{u4} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u3} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u3} R S M (SMulZeroClass.toSMul.{u2, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u2, u3} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u3} S M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u1, u3} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (LinearMap.comp.{u2, u2, u2, max u4 u2, max u4 u2, u3} R R R (α -> R) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) M _inst_2 _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => 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Case conversion may be inaccurate. Consider using '#align finsupp.total_eq_fintype_total Finsupp.total_eq_fintype_totalₓ'. -/
theorem Finsupp.total_eq_fintype_total :
(Finsupp.total α M R v).comp (Finsupp.linearEquivFunOnFinite R R α).symm.toLinearMap =
@@ -1877,7 +1877,7 @@ irreducible_def Span.repr (w : Set M) (x : span R w) : w →₀ R :=
lean 3 declaration is
forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {w : Set.{u2} M} (x : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w)), Eq.{succ u2} M (coeFn.{max (succ (max u2 u1)) (succ u2), max (succ (max u2 u1)) (succ u2)} (LinearMap.{u1, u1, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) w) R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (Finsupp.addCommMonoid.{u2, u1} 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_inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w)) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w)))))) x)
but is expected to have type
- forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {w : Set.{u2} M} (x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) (Span.repr.{u1, u2} R M _inst_1 _inst_2 _inst_3 w x)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} (Set.Elem.{u2} M w) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u1, u1} (Set.Elem.{u2} M w) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) (Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u2} R R (Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} (Set.Elem.{u2} M w) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u1, u1} (Set.Elem.{u2} M w) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} (Set.Elem.{u2} M w) M R _inst_1 _inst_2 _inst_3 (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x w))) (Span.repr.{u1, u2} R M _inst_1 _inst_2 _inst_3 w x)) (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w))) x)
+ forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {w : Set.{u2} M} (x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) (Span.repr.{u1, u2} R M _inst_1 _inst_2 _inst_3 w x)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} (Set.Elem.{u2} M w) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} (Set.Elem.{u2} M w) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) (Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u2} R R (Finsupp.{u2, u1} (Set.Elem.{u2} M w) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} (Set.Elem.{u2} M w) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} (Set.Elem.{u2} M w) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} (Set.Elem.{u2} M w) M R _inst_1 _inst_2 _inst_3 (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x w))) (Span.repr.{u1, u2} R M _inst_1 _inst_2 _inst_3 w x)) (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 w))) x)
Case conversion may be inaccurate. Consider using '#align span.finsupp_total_repr Span.finsupp_total_reprₓ'. -/
@[simp]
theorem Span.finsupp_total_repr {w : Set M} (x : span R w) :
@@ -1891,7 +1891,7 @@ end
/- warning: submodule.finsupp_sum_mem -> Submodule.finsupp_sum_mem is a dubious translation:
lean 3 declaration is
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+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Type.{u3}} {β : Type.{u4}} [_inst_6 : Zero.{u4} β] (S : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (f : Finsupp.{u3, u4} ι β _inst_6) (g : ι -> β -> M), (forall (c : ι), (Ne.{succ u4} β (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (Finsupp.{u3, u4} ι β _inst_6) (fun (_x : Finsupp.{u3, u4} ι β _inst_6) => ι -> β) (Finsupp.coeFun.{u3, u4} ι β _inst_6) f c) (OfNat.ofNat.{u4} β 0 (OfNat.mk.{u4} β 0 (Zero.zero.{u4} β _inst_6)))) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (g c (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (Finsupp.{u3, u4} ι β _inst_6) (fun (_x : Finsupp.{u3, u4} ι β _inst_6) => ι -> β) (Finsupp.coeFun.{u3, u4} ι β _inst_6) f c)) S)) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Finsupp.sum.{u3, u4, u2} ι β M _inst_6 _inst_2 f g) S)
but is expected to have type
forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Type.{u4}} {β : Type.{u3}} [_inst_6 : Zero.{u3} β] (S : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (f : Finsupp.{u4, u3} ι β _inst_6) (g : ι -> β -> M), (forall (c : ι), (Ne.{succ u3} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => β) c) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Finsupp.{u4, u3} ι β _inst_6) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => β) _x) (Finsupp.funLike.{u4, u3} ι β _inst_6) f c) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => β) c) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => β) c) _inst_6))) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) (g c (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Finsupp.{u4, u3} ι β _inst_6) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => β) _x) (Finsupp.funLike.{u4, u3} ι β _inst_6) f c)) S)) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) (Finsupp.sum.{u4, u3, u1} ι β M _inst_6 _inst_2 f g) S)
Case conversion may be inaccurate. Consider using '#align submodule.finsupp_sum_mem Submodule.finsupp_sum_memₓ'. -/
@@ -1904,7 +1904,7 @@ protected theorem Submodule.finsupp_sum_mem {ι β : Type _} [Zero β] (S : Subm
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_4] (f : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M N _inst_2 _inst_4 _inst_3 _inst_5) {ι : Type.{u4}} {g : ι -> M} (l : Finsupp.{u4, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))), Eq.{succ u3} N (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M N _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M N _inst_2 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but is expected to have type
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+ forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u4, u3} R M _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u2} N] [_inst_5 : Module.{u4, u2} R N _inst_1 _inst_4] (f : LinearMap.{u4, u4, u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_2 _inst_4 _inst_3 _inst_5) {ι : Type.{u1}} {g : ι -> M} (l : Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => N) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u1), max (succ u4) (succ u1), succ u3} (LinearMap.{u4, u4, max u4 u1, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u1, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u4, u4} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_3) (Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) (fun (a : Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) => M) a) (LinearMap.instFunLikeLinearMap.{u4, u4, max u4 u1, u3} R R (Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u4, u4} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Finsupp.total.{u1, u3, u4} ι M R _inst_1 _inst_2 _inst_3 g) l)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (LinearMap.{u4, u4, u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_2 _inst_4 _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, u2} R R M N _inst_1 _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) f (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u1), max (succ u4) (succ u1), succ u3} (LinearMap.{u4, u4, max u4 u1, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M (Finsupp.addCommMonoid.{u1, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u4, u4} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_3) (Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) (fun (_x : Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u4 u1, u3} R R (Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u4, u4} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Finsupp.total.{u1, u3, u4} ι M R _inst_1 _inst_2 _inst_3 g) l)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u1), max (succ u4) (succ u1), succ u2} (LinearMap.{u4, u4, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) N (Finsupp.addCommMonoid.{u1, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_4 (Finsupp.module.{u1, u4, u4} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_5) (Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) (fun (_x : Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u4 u1, u2} R R (Finsupp.{u1, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) _inst_4 (Finsupp.module.{u1, u4, u4} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R _inst_1)) _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Finsupp.total.{u1, u2, u4} ι N R _inst_1 _inst_4 _inst_5 (Function.comp.{succ u1, succ u3, succ u2} ι M N (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (LinearMap.{u4, u4, u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_2 _inst_4 _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, u2} R R M N _inst_1 _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) f) g)) l)
Case conversion may be inaccurate. Consider using '#align linear_map.map_finsupp_total LinearMap.map_finsupp_totalₓ'. -/
theorem LinearMap.map_finsupp_total (f : M →ₗ[R] N) {ι : Type _} {g : ι → M} (l : ι →₀ R) :
f (Finsupp.total ι M R g l) = Finsupp.total ι N R (f ∘ g) l := by
@@ -1978,7 +1978,7 @@ theorem mem_span_set {m : M} {s : Set M} :
lean 3 declaration is
forall (R : Type.{u1}) (M : Type.{u2}) (ι : Type.{u3}) [_inst_6 : Semiring.{u1} R] [_inst_7 : Subsingleton.{succ u1} R] [_inst_8 : AddCommMonoid.{u2} M] [_inst_9 : Module.{u1, u2} R M _inst_6 _inst_8], LinearEquiv.{u1, u1, u2, max u3 u1} R R _inst_6 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_6)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_6)) (RingHomInvPair.ids.{u1} R _inst_6) (RingHomInvPair.ids.{u1} R _inst_6) M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_6))))) _inst_8 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_6)))) _inst_9 (Finsupp.module.{u3, u1, u1} ι R R _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_6))) (Semiring.toModule.{u1} R _inst_6))
but is expected to have type
- forall (R : Type.{u1}) (M : Type.{u2}) (ι : Type.{u3}) [_inst_6 : Semiring.{u1} R] [_inst_7 : Subsingleton.{succ u1} R] [_inst_8 : AddCommMonoid.{u2} M] [_inst_9 : Module.{u1, u2} R M _inst_6 _inst_8], LinearEquiv.{u1, u1, u2, max u1 u3} R R _inst_6 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_6)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_6)) (RingHomInvPair.ids.{u1} R _inst_6) (RingHomInvPair.ids.{u1} R _inst_6) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_6))) _inst_8 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_6)))) _inst_9 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} ι R R _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_6))) (Semiring.toModule.{u1} R _inst_6))
+ forall (R : Type.{u1}) (M : Type.{u2}) (ι : Type.{u3}) [_inst_6 : Semiring.{u1} R] [_inst_7 : Subsingleton.{succ u1} R] [_inst_8 : AddCommMonoid.{u2} M] [_inst_9 : Module.{u1, u2} R M _inst_6 _inst_8], LinearEquiv.{u1, u1, u2, max u1 u3} R R _inst_6 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_6)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_6)) (RingHomInvPair.ids.{u1} R _inst_6) (RingHomInvPair.ids.{u1} R _inst_6) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_6))) _inst_8 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_6)))) _inst_9 (Finsupp.module.{u3, u1, u1} ι R R _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_6))) (Semiring.toModule.{u1} R _inst_6))
Case conversion may be inaccurate. Consider using '#align module.subsingleton_equiv Module.subsingletonEquivₓ'. -/
/-- If `subsingleton R`, then `M ≃ₗ[R] ι →₀ R` for any type `ι`. -/
@[simps]
@@ -2004,7 +2004,7 @@ open Finsupp Function
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_1 _inst_1 _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3)
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} (f : LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u1) (succ u3)} M (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u3} R R M (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _inst_1 _inst_1 _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} (f : LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u1) (succ u3)} M (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u3} R R M (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _inst_1 _inst_1 _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3)
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_finsupp_surjective LinearMap.splittingOfFinsuppSurjectiveₓ'. -/
-- See also `linear_map.splitting_of_fun_on_fintype_surjective`
/-- A surjective linear map to finitely supported functions has a splitting. -/
@@ -2016,7 +2016,7 @@ def splittingOfFinsuppSurjective (f : M →ₗ[R] α →₀ R) (s : Surjective f
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_1 _inst_1 _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Eq.{succ (max u3 u1)} (LinearMap.{u1, u1, max u3 u1, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (LinearMap.comp.{u1, u1, u1, max u3 u1, u2, max u3 u1} R R R (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomCompTriple.right_ids.{u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f (LinearMap.splittingOfFinsuppSurjective.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 α f s)) (LinearMap.id.{u1, max u3 u1} R (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))
but is expected to have type
- forall {R : Type.{u3}} {M : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u3, u2} R M _inst_1 _inst_2] {α : Type.{u1}} (f : LinearMap.{u3, u3, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u2, max (succ u3) (succ u1)} (LinearMap.{u3, u3, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, max u3 u1} R R M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_1 _inst_1 _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)), Eq.{max (succ u3) (succ u1)} (LinearMap.{u3, u3, max u3 u1, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (LinearMap.comp.{u3, u3, u3, max u3 u1, u2, max u3 u1} R R R (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomCompTriple.ids.{u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f (LinearMap.splittingOfFinsuppSurjective.{u3, u2, u1} R M _inst_1 _inst_2 _inst_3 α f s)) (LinearMap.id.{u3, max u3 u1} R (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)))
+ forall {R : Type.{u3}} {M : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u3, u2} R M _inst_1 _inst_2] {α : Type.{u1}} (f : LinearMap.{u3, u3, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u2, max (succ u3) (succ u1)} (LinearMap.{u3, u3, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, max u3 u1} R R M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_1 _inst_1 _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)), Eq.{max (succ u3) (succ u1)} (LinearMap.{u3, u3, max u3 u1, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (LinearMap.comp.{u3, u3, u3, max u3 u1, u2, max u3 u1} R R R (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomCompTriple.ids.{u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f (LinearMap.splittingOfFinsuppSurjective.{u3, u2, u1} R M _inst_1 _inst_2 _inst_3 α f s)) (LinearMap.id.{u3, max u3 u1} R (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)))
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_finsupp_surjective_splits LinearMap.splittingOfFinsuppSurjective_splitsₓ'. -/
theorem splittingOfFinsuppSurjective_splits (f : M →ₗ[R] α →₀ R) (s : Surjective f) :
f.comp (splittingOfFinsuppSurjective f s) = LinearMap.id :=
@@ -2033,7 +2033,7 @@ theorem splittingOfFinsuppSurjective_splits (f : M →ₗ[R] α →₀ R) (s : S
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M 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but is expected to have type
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_2 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.splittingOfFinsuppSurjective.{u3, u2, u1} R M _inst_1 _inst_2 _inst_3 α f s))
+ forall {R : Type.{u3}} {M : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u3, u2} R M _inst_1 _inst_2] {α : Type.{u1}} (f : LinearMap.{u3, u3, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u2, max (succ u3) (succ u1)} (LinearMap.{u3, u3, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, max u3 u1} R R M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_1 _inst_1 _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)), Function.LeftInverse.{max (succ u3) (succ u1), succ u2} (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u2, max (succ u3) (succ u1)} (LinearMap.{u3, u3, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, max u3 u1} R R M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_1 _inst_1 _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u1), succ u2} (LinearMap.{u3, u3, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_3) (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (fun (_x : Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u1, u2} R R (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.splittingOfFinsuppSurjective.{u3, u2, u1} R M _inst_1 _inst_2 _inst_3 α f s))
Case conversion may be inaccurate. Consider using '#align linear_map.left_inverse_splitting_of_finsupp_surjective LinearMap.leftInverse_splittingOfFinsuppSurjectiveₓ'. -/
theorem leftInverse_splittingOfFinsuppSurjective (f : M →ₗ[R] α →₀ R) (s : Surjective f) :
LeftInverse f (splittingOfFinsuppSurjective f s) := fun g =>
@@ -2044,7 +2044,7 @@ theorem leftInverse_splittingOfFinsuppSurjective (f : M →ₗ[R] α →₀ R) (
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_1 _inst_1 _inst_2 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Function.Injective.{max (succ u3) (succ u1), succ u2} (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) (fun (_x : LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) => (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.splittingOfFinsuppSurjective.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 α f s))
but is expected to have type
- forall {R : Type.{u3}} {M : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u3, u2} R M _inst_1 _inst_2] {α : Type.{u1}} (f : LinearMap.{u3, u3, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u2, max (succ u3) (succ u1)} (LinearMap.{u3, u3, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, max u3 u1} R R M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_1 _inst_1 _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)), Function.Injective.{max (succ u3) (succ u1), succ u2} (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u1), succ u2} (LinearMap.{u3, u3, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_2 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_3) (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (fun (_x : Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u1, u2} R R (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_2 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.splittingOfFinsuppSurjective.{u3, u2, u1} R M _inst_1 _inst_2 _inst_3 α f s))
+ forall {R : Type.{u3}} {M : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u3, u2} R M _inst_1 _inst_2] {α : Type.{u1}} (f : LinearMap.{u3, u3, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u2, max (succ u3) (succ u1)} (LinearMap.{u3, u3, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, max u3 u1} R R M (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_1 _inst_1 _inst_2 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)), Function.Injective.{max (succ u3) (succ u1), succ u2} (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u1), succ u2} (LinearMap.{u3, u3, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_3) (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (fun (_x : Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u1, u2} R R (Finsupp.{u1, u3} α R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.splittingOfFinsuppSurjective.{u3, u2, u1} R M _inst_1 _inst_2 _inst_3 α f s))
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_finsupp_surjective_injective LinearMap.splittingOfFinsuppSurjective_injectiveₓ'. -/
theorem splittingOfFinsuppSurjective_injective (f : M →ₗ[R] α →₀ R) (s : Surjective f) :
Injective (splittingOfFinsuppSurjective f s) :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/195fcd60ff2bfe392543bceb0ec2adcdb472db4c
@@ -576,7 +576,7 @@ variable (S) [Module S N] [SMulCommClass R S N]
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toHasSmul.{u4, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u4, u3} R N (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u5, u3} S N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u5, u3} S N (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))], LinearEquiv.{u5, u5, max u1 u2 u3, max (max u1 u2) u3} S S _inst_2 _inst_2 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2) (α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u1, max u2 u3} α (fun (ᾰ : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.Function.module.{u1, u5, max u2 u3} α S (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.module.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.module.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)
but is expected to have type
- forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toSMul.{u4, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u4, u3} R N (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u5, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} S N (MonoidWithZero.toZero.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))], LinearEquiv.{u5, u5, max (max u1 u2) u3, max u3 u2 u1} S S _inst_2 _inst_2 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2) (α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u4, u4, max u2 u1, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u1, max u2 u3} α (fun (ᾰ : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.module.{u1, max u2 u3, u5} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)
+ forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toSMul.{u4, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u4, u3} R N (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u5, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} S N (MonoidWithZero.toZero.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))], LinearEquiv.{u5, u5, max (max u1 u2) u3, max u3 u2 u1} S S _inst_2 _inst_2 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2) (α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u4, u4, max u2 u1, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u1, max u2 u3} α (fun (ᾰ : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.module.{u1, max u2 u3, u5} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)
Case conversion may be inaccurate. Consider using '#align finsupp.lsum Finsupp.lsumₓ'. -/
/-- Lift a family of linear maps `M →ₗ[R] N` indexed by `x : α` to a linear map from `α →₀ M` to
`N` using `finsupp.sum`. This is an upgraded version of `finsupp.lift_add_hom`.
@@ -608,7 +608,7 @@ def lsum : (α → M →ₗ[R] N) ≃ₗ[S] (α →₀ M) →ₗ[R] N
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toHasSmul.{u4, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u4, u3} R N (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u5, u3} S N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u5, u3} S N (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)), Eq.{max (max (succ u1) (succ u2)) (succ u3)} ((fun (_x : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) => (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) -> N) (coeFn.{max (succ (max u1 u2 u3)) (succ (max (max u1 u2) u3)), max (succ (max u1 u2 u3)) (succ (max (max u1 u2) u3))} (LinearEquiv.{u5, u5, max u1 u2 u3, max (max u1 u2) u3} S S _inst_2 _inst_2 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S 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=> LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.Function.module.{u1, u5, max u2 u3} α S (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.module.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.module.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2)) (Finsupp.lsum.{u1, u2, u3, u4, u5} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f)) (fun (d : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) => Finsupp.sum.{u1, u2, u3} α M N (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_5 d (fun (i : α) => coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (_x : LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) => M -> N) (LinearMap.hasCoeToFun.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (f i)))
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u4}} {N : Type.{u3}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u3} R S N (SMulZeroClass.toSMul.{u5, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)), Eq.{max (max (succ u2) (succ u4)) (succ u3)} (forall (a : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) a) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) 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_inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (fun (_x : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _x) (SMulHomClass.toFunLike.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2} S S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f)) (fun (d : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => Finsupp.sum.{u2, u4, u3} α M ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) d) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) _inst_5 d (fun (i : α) => FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f i)))
+ forall {α : Type.{u2}} {M : Type.{u4}} {N : Type.{u3}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u3} R S N (SMulZeroClass.toSMul.{u5, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)), Eq.{max (max (succ u2) (succ u4)) (succ u3)} (forall (a : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) a) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) f) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (fun (_x : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (fun (_x : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _x) (SMulHomClass.toFunLike.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 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(Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f)) (fun (d : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => Finsupp.sum.{u2, u4, u3} α M ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) d) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) _inst_5 d (fun (i : α) => FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f i)))
Case conversion may be inaccurate. Consider using '#align finsupp.coe_lsum Finsupp.coe_lsumₓ'. -/
@[simp]
theorem coe_lsum (f : α → M →ₗ[R] N) : (lsum S f : (α →₀ M) → N) = fun d => d.Sum fun i => f i :=
@@ -619,7 +619,7 @@ theorem coe_lsum (f : α → M →ₗ[R] N) : (lsum S f : (α →₀ M) → N) =
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toHasSmul.{u4, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u4, u3} R N (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u5, u3} S N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u5, u3} S N (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (l : Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))), Eq.{succ u3} N (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (fun (_x : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 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(Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u1, max u2 u3} α (fun (ᾰ : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.Function.module.{u1, u5, max u2 u3} α S (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 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M N _inst_3 _inst_5 _inst_4 _inst_6)) -> (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6)) (LinearEquiv.hasCoeToFun.{u5, u5, max u1 u2 u3, max (max u1 u2) u3} S S (α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u1, max u2 u3} α (fun (ᾰ : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.Function.module.{u1, u5, max u2 u3} α S (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.module.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.module.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2)) (Finsupp.lsum.{u1, u2, u3, u4, u5} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f) l) (Finsupp.sum.{u1, u2, u3} α M N (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_5 l (fun (b : α) => coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (_x : LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) => M -> N) (LinearMap.hasCoeToFun.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (f b)))
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u4}} {N : Type.{u3}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u3} R S N (SMulZeroClass.toSMul.{u5, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (l : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) l) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), succ u3} ((fun 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_inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (fun (_x : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _x) (SMulHomClass.toFunLike.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2} S S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f) l) (Finsupp.sum.{u2, u4, u3} α M N (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) _inst_5 l (fun (b : α) => FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f b)))
+ forall {α : Type.{u2}} {M : Type.{u4}} {N : Type.{u3}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u3} R S N (SMulZeroClass.toSMul.{u5, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (l : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) l) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) f) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (fun (_x : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R 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(Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (fun (_x : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _x) (SMulHomClass.toFunLike.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => 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(Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f) l) (Finsupp.sum.{u2, u4, u3} α M N (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) _inst_5 l (fun (b : α) => FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f b)))
Case conversion may be inaccurate. Consider using '#align finsupp.lsum_apply Finsupp.lsum_applyₓ'. -/
theorem lsum_apply (f : α → M →ₗ[R] N) (l : α →₀ M) : Finsupp.lsum S f l = l.Sum fun b => f b :=
rfl
@@ -629,7 +629,7 @@ theorem lsum_apply (f : α → M →ₗ[R] N) (l : α →₀ M) : Finsupp.lsum S
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toHasSmul.{u4, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u4, u3} R N (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u5, u3} S N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u5, u3} S N (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (i : α) (m : M), Eq.{succ u3} N (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (fun (_x : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) => (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) -> N) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (coeFn.{max (succ (max u1 u2 u3)) (succ (max (max u1 u2) u3)), max (succ (max u1 u2 u3)) (succ (max (max u1 u2) u3))} (LinearEquiv.{u5, u5, max u1 u2 u3, max (max u1 u2) u3} S S _inst_2 _inst_2 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2) (α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) 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(AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) i m)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (_x : LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) => M -> N) (LinearMap.hasCoeToFun.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (f i) m)
but is expected to have type
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(Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (fun (_x : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _x) (SMulHomClass.toFunLike.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => 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_inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R 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(Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2} S S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f) (Finsupp.single.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) i m)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f i) m)
+ forall {α : Type.{u2}} {M : Type.{u4}} {N : Type.{u3}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u5, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u3} R S N (SMulZeroClass.toSMul.{u5, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u3} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u3} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u5, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} S N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (Module.toMulActionWithZero.{u1, u3} S N _inst_2 _inst_5 _inst_9))))] (f : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (i : α) (m : M), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) => N) (Finsupp.single.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) i m)) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), succ u3} 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u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (fun (_x : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) => LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _x) (SMulHomClass.toFunLike.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (SMulZeroClass.toSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u1, max (max u3 u4) u2, max (max u3 u4) u2} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u4) u2} (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (Module.toDistribMulAction.{u1, max (max u3 u4) u2} S (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max u3 u4 u2} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => 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LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2, max (max u3 u4) u2} S S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 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(Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u3 u4) u2, max (max u3 u4) u2} S S (α -> (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u2, max u4 u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u2 u4, u3} R R (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u2, max u4 u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u2 u4, u3} R R S (Finsupp.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (Finsupp.lsum.{u2, u4, u3, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10) f) (Finsupp.single.{u2, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) i m)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f i) m)
Case conversion may be inaccurate. Consider using '#align finsupp.lsum_single Finsupp.lsum_singleₓ'. -/
theorem lsum_single (f : α → M →ₗ[R] N) (i : α) (m : M) :
Finsupp.lsum S f (Finsupp.single i m) = f i m :=
@@ -640,7 +640,7 @@ theorem lsum_single (f : α → M →ₗ[R] N) (i : α) (m : M) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {R : Type.{u4}} (S : Type.{u5}) [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u5} S] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u4, u2} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u4, u3} R N _inst_1 _inst_5] [_inst_9 : Module.{u5, u3} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u4, u5, u3} R S N (SMulZeroClass.toHasSmul.{u4, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u4, u3} R N (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_1)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u4, u3} R N (Semiring.toMonoidWithZero.{u4} R _inst_1) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u4, u3} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u5, u3} S N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u5, u3} S N (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_2)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u5, u3} S N (Semiring.toMonoidWithZero.{u5} S _inst_2) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u5, u3} S N _inst_2 _inst_5 _inst_9))))] (f : LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (x : α), Eq.{max (succ u2) (succ u3)} (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (coeFn.{max (succ (max (max u1 u2) u3)) (succ (max u1 u2 u3)), max (succ (max (max u1 u2) u3)) (succ (max u1 u2 u3))} (LinearEquiv.{u5, u5, max (max u1 u2) u3, max u1 u2 u3} S S _inst_2 _inst_2 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2) (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.addCommMonoid.{u1, max u2 u3} α (fun (ᾰ : α) => LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)))) (LinearMap.module.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.Function.module.{u1, u5, max u2 u3} α S (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.module.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10))) (fun (_x : LinearEquiv.{u5, u5, max (max u1 u2) u3, max u1 u2 u3} S S _inst_2 _inst_2 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2) (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u4, u4, max u1 u2, 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u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) -> α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearEquiv.hasCoeToFun.{u5, u5, max (max u1 u2) u3, max u1 u2 u3} S S (LinearMap.{u4, u4, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 _inst_2 (LinearMap.addCommMonoid.{u4, u4, max u1 u2, u3} R R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M 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(AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Pi.Function.module.{u1, u5, max u2 u3} α S (LinearMap.{u4, u4, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u2, u3} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (LinearMap.module.{u4, u4, u5, u2, u3} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.module.{u4, u4, u5, max u1 u2, u3} R R S (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_2)) (RingHomInvPair.ids.{u5} S _inst_2) (RingHomInvPair.ids.{u5} S _inst_2) (Finsupp.lsum.{u1, u2, u3, u4, u5} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10)) f x) (LinearMap.comp.{u4, u4, u4, u2, max u1 u2, u3} R R R M (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) N _inst_1 _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) _inst_5 _inst_4 (Finsupp.module.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHomCompTriple.right_ids.{u4, u4} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) f (Finsupp.lsingle.{u1, u2, u4} α M R _inst_1 _inst_3 _inst_4 x))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u4}} {N : Type.{u2}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : Module.{u5, u2} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u2} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u2} R S N (SMulZeroClass.toSMul.{u5, u2} R N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u2} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u2} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (Module.toMulActionWithZero.{u5, u2} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u2} S N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u2} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u2} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (Module.toMulActionWithZero.{u1, u2} S N _inst_2 _inst_5 _inst_9))))] (f : LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (x : α), Eq.{max (succ u4) (succ u2)} (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N 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(Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u4) u3, u1, max (max u2 u4) u3, max (max u2 u4) u3} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u2 u4) u3, max (max u2 u4) u3, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3, max (max u2 u4) u3} S S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) _inst_2 _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (LinearEquiv.symm.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (ᾰ : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4410 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (Finsupp.lsum.{u3, u4, u2, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10)) f x) (LinearMap.comp.{u5, u5, u5, u4, max u3 u4, u2} R R R M (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 _inst_4 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHomCompTriple.ids.{u5, u5} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) f (Finsupp.lsingle.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4 x))
+ forall {α : Type.{u3}} {M : Type.{u4}} {N : Type.{u2}} {R : Type.{u5}} (S : Type.{u1}) [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u1} S] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 _inst_3] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : Module.{u5, u2} R N _inst_1 _inst_5] [_inst_9 : Module.{u1, u2} S N _inst_2 _inst_5] [_inst_10 : SMulCommClass.{u5, u1, u2} R S N (SMulZeroClass.toSMul.{u5, u2} R N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u2} R N (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u2} R N (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (Module.toMulActionWithZero.{u5, u2} R N _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u2} S N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u2} S N (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u2} S N (Semiring.toMonoidWithZero.{u1} S _inst_2) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (Module.toMulActionWithZero.{u1, u2} S N _inst_2 _inst_5 _inst_9))))] (f : LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (x : α), Eq.{max (succ u4) (succ u2)} (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (max (succ u2) (succ u4)) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (fun (_x : LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) => α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _x) (SMulHomClass.toFunLike.{max (max u2 u4) u3, u1, max (max u2 u4) u3, max (max u2 u4) u3} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (SMulZeroClass.toSMul.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toZero.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))))) (SMulZeroClass.toSMul.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toZero.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddMonoid.toAddZeroClass.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u4) u3, u1, max (max u2 u4) u3, max (max u2 u4) u3} (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_2)) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u3} (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (Module.toDistribMulAction.{u1, max (max u2 u4) u3} S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u2 u4) u3, max (max u2 u4) u3, max (max u2 u4) u3} S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S _inst_2 _inst_2 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R 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_inst_10))) _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M 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(Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10))) _inst_2 _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (Pi.module.{u3, max u4 u2, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) S _inst_2 (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) _inst_2 _inst_2 (LinearMap.addCommMonoid.{u5, u5, max u3 u4, u2} R R (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Pi.addCommMonoid.{u3, max u4 u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4414 : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6) (fun (i : α) => LinearMap.addCommMonoid.{u5, u5, u4, u2} R R M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, 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(Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2)))))) (LinearEquiv.symm.{u1, u1, max (max u2 u4) u3, max (max u2 u4) u3} S S (α -> (LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M N _inst_3 _inst_5 _inst_4 _inst_6)) (LinearMap.{u5, u5, max u4 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, max u4 u2} α (fun (ᾰ : α) => LinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 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_inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (fun (i : α) => LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, u4, u2} R R S M N _inst_1 _inst_1 _inst_3 _inst_5 _inst_4 _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10)) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u1, max u3 u4, u2} R R S (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_2 _inst_9 _inst_10) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomInvPair.ids.{u1} S _inst_2) (RingHomInvPair.ids.{u1} S _inst_2) (Finsupp.lsum.{u3, u4, u2, u5, u1} α M N R S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10)) f x) (LinearMap.comp.{u5, u5, u5, u4, max u3 u4, u2} R R R M (Finsupp.{u3, u4} α M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) N _inst_1 _inst_1 _inst_1 _inst_3 (Finsupp.addCommMonoid.{u3, u4} α M _inst_3) _inst_5 _inst_4 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4) _inst_6 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHomCompTriple.ids.{u5, u5} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) f (Finsupp.lsingle.{u3, u4, u5} α M R _inst_1 _inst_3 _inst_4 x))
Case conversion may be inaccurate. Consider using '#align finsupp.lsum_symm_apply Finsupp.lsum_symm_applyₓ'. -/
theorem lsum_symm_apply (f : (α →₀ M) →ₗ[R] N) (x : α) : (lsum S).symm f x = f.comp (lsingle x) :=
rfl
@@ -670,7 +670,7 @@ noncomputable def lift : (X → M) ≃+ ((X →₀ R) →ₗ[R] M) :=
lean 3 declaration is
forall (M : Type.{u1}) (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u3}) (f : LinearMap.{u2, u2, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.module.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (x : X), Eq.{succ u1} M (coeFn.{max (succ (max (max u3 u2) u1)) (succ 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but is expected to have type
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => X -> M) _x) (AddHomClass.toFunLike.{max (max u1 u3) u2, max (max u1 u3) u2, max u1 u2} (AddEquiv.{max (max u1 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(RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (AddZeroClass.toAdd.{max u1 u2} (X -> M) (Pi.addZeroClass.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (AddMonoidHomClass.toAddHomClass.{max (max u1 u3) u2, max (max u1 u3) u2, max u1 u2} (AddEquiv.{max (max u1 u3) u2, max u1 u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (LinearMap.instAddLinearMap.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R 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(MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Pi.addZeroClass.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddEquivClass.instAddMonoidHomClass.{max (max u1 u3) u2, max (max u1 u3) u2, max u1 u2} (AddEquiv.{max (max u1 u3) u2, max u1 u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (LinearMap.instAddLinearMap.{u3, u3, max u3 u2, u1} R R (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.instAdd.{u2, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (X -> M) (AddMonoid.toAddZeroClass.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u3, u3} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u2, u3} X R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u3} X R 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Case conversion may be inaccurate. Consider using '#align finsupp.lift_symm_apply Finsupp.lift_symm_applyₓ'. -/
@[simp]
theorem lift_symm_apply (f) (x) : ((lift M R X).symm f) x = f (single x 1) :=
@@ -681,7 +681,7 @@ theorem lift_symm_apply (f) (x) : ((lift M R X).symm f) x = f (single x 1) :=
lean 3 declaration is
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(AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddZeroClass.toHasZero.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4)))) r (f x)))
but is expected to have type
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddEquiv.instAddEquivClassAddEquiv.{max u1 u3, max (max u1 u2) u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4916 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (Finsupp.lift.{u1, u2, u3} M R _inst_1 _inst_3 _inst_4 X) f) g) (Finsupp.sum.{u3, u2, u1} X R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) _inst_3 g (fun (x : X) (r : R) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4))))) r (f x)))
+ forall (M : Type.{u1}) (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (X : Type.{u3}) (f : X -> M) (g : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) g) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : X -> M) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R 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(Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R 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(AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddZeroClass.toAdd.{max u1 u3} (X -> M) (Pi.addZeroClass.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (AddZeroClass.toAdd.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (AddMonoidHomClass.toAddHomClass.{max (max u1 u2) u3, max u1 u3, max (max u1 u2) u3} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.addZeroClass.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddEquivClass.instAddMonoidHomClass.{max (max u1 u2) u3, max u1 u3, max (max u1 u2) u3} (AddEquiv.{max u1 u3, max u1 u2 u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.addZeroClass.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddEquiv.instAddEquivClassAddEquiv.{max u1 u3, max (max u1 u2) u3} (X -> M) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Pi.instAdd.{u3, u1} X (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.4920 : X) => M) (fun (i : X) => AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (LinearMap.instAddLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} X R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} X R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} X R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (Finsupp.lift.{u1, u2, u3} M R _inst_1 _inst_3 _inst_4 X) f) g) (Finsupp.sum.{u3, u2, u1} X R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) _inst_3 g (fun (x : X) (r : R) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_3 _inst_4))))) r (f x)))
Case conversion may be inaccurate. Consider using '#align finsupp.lift_apply Finsupp.lift_applyₓ'. -/
@[simp]
theorem lift_apply (f) (g) : ((lift M R X) f) g = g.Sum fun x r => r • f x :=
@@ -898,7 +898,7 @@ theorem total_single (c : R) (a : α) : Finsupp.total α M R v (single a c) = c
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (x : Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) => (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u1 u2} (α -> M) 0 (OfNat.mk.{max u1 u2} (α -> M) 0 (Zero.zero.{max u1 u2} (α -> M) (Pi.instZero.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))))))) x) (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))))))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u3 u1} (α -> M) 0 (Zero.toOfNat0.{max u3 u1} (α -> M) (Pi.instZero.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.6471 : α) => M) (fun (i : α) => AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) _inst_3))))
+ forall {α : Type.{u3}} {M : Type.{u1}} (R : Type.{u2}) [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4) (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u3 u1} (α -> M) 0 (Zero.toOfNat0.{max u3 u1} (α -> M) (Pi.instZero.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.6475 : α) => M) (fun (i : α) => AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) x) _inst_3))))
Case conversion may be inaccurate. Consider using '#align finsupp.total_zero_apply Finsupp.total_zero_applyₓ'. -/
theorem total_zero_apply (x : α →₀ R) : (Finsupp.total α M R 0) x = 0 := by
simp [Finsupp.total_apply]
@@ -910,7 +910,7 @@ variable (α M)
lean 3 declaration is
forall (α : Type.{u1}) (M : Type.{u2}) (R : Type.{u3}) [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3], Eq.{max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (Finsupp.total.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u1 u2} (α -> M) 0 (OfNat.mk.{max u1 u2} (α -> M) 0 (Zero.zero.{max u1 u2} (α -> M) (Pi.instZero.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))))))) (OfNat.ofNat.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) 0 (OfNat.mk.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) 0 (Zero.zero.{max (max u1 u3) u2} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4) (LinearMap.hasZero.{u3, u3, max u1 u3, u2} R R (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) _inst_3 (Finsupp.module.{u1, u3, u3} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))))
but is expected to have type
- forall (α : Type.{u3}) (M : Type.{u2}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Eq.{max (max (succ u3) (succ u2)) (succ u1)} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u3 u2} (α -> M) 0 (Zero.toOfNat0.{max u3 u2} (α -> M) (Pi.instZero.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.6471 : α) => M) (fun (i : α) => AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))))) (OfNat.ofNat.{max (max u3 u2) u1} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) 0 (Zero.toOfNat0.{max (max u3 u2) u1} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (LinearMap.instZeroLinearMap.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))
+ forall (α : Type.{u3}) (M : Type.{u2}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Eq.{max (max (succ u3) (succ u2)) (succ u1)} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (Finsupp.total.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{max u3 u2} (α -> M) 0 (Zero.toOfNat0.{max u3 u2} (α -> M) (Pi.instZero.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.6475 : α) => M) (fun (i : α) => AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))))) (OfNat.ofNat.{max (max u3 u2) u1} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) 0 (Zero.toOfNat0.{max (max u3 u2) u1} (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4) (LinearMap.instZeroLinearMap.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} α R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u1} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))
Case conversion may be inaccurate. Consider using '#align finsupp.total_zero Finsupp.total_zeroₓ'. -/
@[simp]
theorem total_zero : Finsupp.total α M R 0 = 0 :=
@@ -1749,7 +1749,7 @@ variable {S}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] {S : Type.{u4}} [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (f : α -> R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) => (α -> R) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (coeFn.{max (succ (max u1 u2)) (succ (max (max u1 u3) u2)), max (succ (max u1 u2)) (succ (max (max u1 u3) u2))} (LinearMap.{u4, u4, max u1 u2, max (max u1 u3) u2} S S _inst_5 _inst_5 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) => (α -> M) -> (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4)) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, max (max u1 u3) u2} S S (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) f) (Finset.sum.{u2, u1} M α _inst_3 (Finset.univ.{u1} α _inst_1) (fun (i : α) => SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (f i) (v i)))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (f : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> R) => M) f) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) v) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearMap.{u1, u1, max u3 u4, max u4 u3 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u3, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13961 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 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(Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13961 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) f) (Finset.sum.{u4, u3} M α _inst_3 (Finset.univ.{u3} α _inst_1) (fun (i : α) => HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) (f i) (v i)))
+ forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (f : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> R) => M) f) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) v) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearMap.{u1, u1, max u3 u4, max u4 u3 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u3, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13965 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13965 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13965 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) f) (Finset.sum.{u4, u3} M α _inst_3 (Finset.univ.{u3} α _inst_1) (fun (i : α) => HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) (f i) (v i)))
Case conversion may be inaccurate. Consider using '#align fintype.total_apply Fintype.total_applyₓ'. -/
theorem Fintype.total_apply (f) : Fintype.total R S v f = ∑ i, f i • v i :=
rfl
@@ -1759,7 +1759,7 @@ theorem Fintype.total_apply (f) : Fintype.total R S v f = ∑ i, f i • v i :=
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] {S : Type.{u4}} [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (i : α) (r : R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R 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(Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) (Pi.single.{u1, u3} α (fun (ᾰ : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u1} α a b)) (fun (i : α) => MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) i r)) (SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) r (v i))
but is expected to have type
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(MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (i : α) (r : R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> R) => M) (Pi.single.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u3, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13961 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13961 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13961 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) (Pi.single.{u3, u2} α (fun (ᾰ : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) r (v i))
+ forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (i : α) (r : R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> R) => M) (Pi.single.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) v) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), max (max (succ u2) (succ u4)) (succ u3)} (LinearMap.{u1, u1, max u3 u4, max u4 u3 u2} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u3, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13965 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13965 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13965 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) (Pi.single.{u3, u2} α (fun (ᾰ : α) => R) (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) (fun (i : α) => MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) i r)) (HSMul.hSMul.{u2, u4, u4} R M M (instHSMul.{u2, u4} R M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4))))) r (v i))
Case conversion may be inaccurate. Consider using '#align fintype.total_apply_single Fintype.total_apply_singleₓ'. -/
@[simp]
theorem Fintype.total_apply_single (i : α) (r : R) :
@@ -1775,7 +1775,7 @@ variable (S)
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] (S : Type.{u4}) [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (x : α -> R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R 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(Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) (fun (_x : LinearMap.{u4, u4, max u1 u2, max (max u1 u3) u2} S S _inst_5 _inst_5 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) => (α -> M) -> (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4)) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, max (max u1 u3) u2} S S (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) x)
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (x : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) => M) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (α -> R) (fun (a : α -> R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> R) => Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) a) (SMulHomClass.toFunLike.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (α -> R) (AddMonoid.toZero.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (α -> R) (AddMonoid.toAddZeroClass.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (α -> R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u3 u2, max u3 u2, max u3 u2} R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : 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(Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 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(a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u3 u2, max u3 u2, max u3 u2} R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun 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(SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u3 u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R 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(α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u3, max (max u2 u4) u3} S S (α -> M) (LinearMap.{u2, u2, max u3 u2, u4} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u3, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u3, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13961 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u3 u2, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) x)
+ forall {α : Type.{u3}} {M : Type.{u4}} (R : Type.{u2}) [_inst_1 : Fintype.{u3} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u2, u4} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u4} R S M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M) (x : α -> R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) => M) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (α -> R) (fun (a : α -> R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : α -> R) => Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) a) (SMulHomClass.toFunLike.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (α -> R) (AddMonoid.toZero.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (α -> R) (AddMonoid.toAddZeroClass.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (α -> R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u3 u2, max u3 u2, max u3 u2} R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (α -> R) (AddMonoid.toZero.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (α -> R) (AddMonoid.toAddZeroClass.{max u3 u2} (α -> R) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (α -> R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{max u3 u2} (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))))) (Module.toDistribMulAction.{u2, max u3 u2} R (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u3 u2, max u3 u2, max u3 u2} R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u3 u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (LinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2))) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max u3 u2, max u3 u2} R R (α -> R) (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u3, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2)))))) (LinearEquiv.symm.{u2, u2, max u3 u2, max u3 u2} R R (Finsupp.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (α -> R) _inst_2 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NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u3, u4, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v) x)
Case conversion may be inaccurate. Consider using '#align finsupp.total_eq_fintype_total_apply Finsupp.total_eq_fintype_total_applyₓ'. -/
theorem Finsupp.total_eq_fintype_total_apply (x : α → R) :
Finsupp.total α M R v ((Finsupp.linearEquivFunOnFinite R R α).symm x) = Fintype.total R S v x :=
@@ -1791,7 +1791,7 @@ theorem Finsupp.total_eq_fintype_total_apply (x : α → R) :
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] (S : Type.{u4}) [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (LinearMap.comp.{u3, u3, u3, max u1 u3, max u1 u3, u2} R R R (α -> R) (Finsupp.{u1, u3} α R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))) M _inst_2 _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) (Finsupp.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHomCompTriple.right_ids.{u3, u3} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Finsupp.total.{u1, u2, u3} α M R _inst_2 _inst_3 _inst_4 v) (LinearEquiv.toLinearMap.{u3, u3, max u1 u3, max u1 u3} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (RingHomInvPair.ids.{u3} R _inst_2) (RingHomInvPair.ids.{u3} R _inst_2) (α -> R) (Finsupp.{u1, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))))))) (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Finsupp.addCommMonoid.{u1, u3} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) (Pi.Function.module.{u1, 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(Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)
but is expected to have type
- forall {α : Type.{u4}} {M : Type.{u3}} (R : Type.{u2}) [_inst_1 : Fintype.{u4} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u3} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u3} R S M (SMulZeroClass.toSMul.{u2, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u2, u3} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u3} S M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u1, u3} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (LinearMap.comp.{u2, u2, u2, max u4 u2, max u4 u2, u3} R R R (α -> R) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) M _inst_2 _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => 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(AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (LinearEquiv.symm.{u2, u2, max u4 u2, max u4 u2} R R (Finsupp.{u4, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (α -> R) _inst_2 _inst_2 (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u2} α R R _inst_2 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(a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13961 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u4 u2, u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u4, u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13961 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u4 u2, u3} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R 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(Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u4, u3} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u2, u2, max u4 u2, u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u4, u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13961 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u4 u2, u3} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u4, u3, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)
+ forall {α : Type.{u4}} {M : Type.{u3}} (R : Type.{u2}) [_inst_1 : Fintype.{u4} α] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_2 _inst_3] (S : Type.{u1}) [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u3} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u2, u1, u3} R S M (SMulZeroClass.toSMul.{u2, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u2, u3} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u3} S M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3)) (Module.toMulActionWithZero.{u1, u3} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (LinearMap.{u2, u2, max u4 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4) (LinearMap.comp.{u2, u2, u2, max u4 u2, max u4 u2, u3} R R R (α -> R) (Finsupp.{u4, u2} α R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2))) M _inst_2 _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomCompTriple.ids.{u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Finsupp.total.{u4, u3, u2} α M R _inst_2 _inst_3 _inst_4 v) (LinearEquiv.toLinearMap.{u2, u2, max u4 u2, max u4 u2} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (α -> R) (Finsupp.{u4, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (LinearEquiv.symm.{u2, u2, max u4 u2, max u4 u2} R R (Finsupp.{u4, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))))) (α -> R) _inst_2 _inst_2 (Finsupp.addCommMonoid.{u4, u2} α R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u2} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Basic._hyg.427 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (Finsupp.linearEquivFunOnFinite.{u2, u2, u4} R R α (Finite.of_fintype.{u4} α _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) _inst_2 (Semiring.toModule.{u2} R _inst_2))))) (FunLike.coe.{max 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(Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Pi.module.{u4, u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13965 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, max u4 u2, u3} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u4, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_3 (Pi.module.{u4, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : α) => Semiring.toModule.{u2} R _inst_2)) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u4, u3, u2, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)
Case conversion may be inaccurate. Consider using '#align finsupp.total_eq_fintype_total Finsupp.total_eq_fintype_totalₓ'. -/
theorem Finsupp.total_eq_fintype_total :
(Finsupp.total α M R v).comp (Finsupp.linearEquivFunOnFinite R R α).symm.toLinearMap =
@@ -1805,7 +1805,7 @@ variable {S}
lean 3 declaration is
forall {α : Type.{u1}} {M : Type.{u2}} (R : Type.{u3}) [_inst_1 : Fintype.{u1} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_2 _inst_3] {S : Type.{u4}} [_inst_5 : Semiring.{u4} S] [_inst_6 : Module.{u4, u2} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u4, u2} R S M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u3, u2} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_5)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M (Semiring.toMonoidWithZero.{u4} S _inst_5) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u4, u2} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{succ u2} (Submodule.{u3, u2} R M _inst_2 _inst_3 _inst_4) (LinearMap.range.{u3, u3, max u1 u3, u2, max (max u1 u3) u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (LinearMap.semilinearMapClass.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (RingHomSurjective.ids.{u3} R _inst_2) (coeFn.{max (succ (max u1 u2)) (succ (max (max u1 u3) u2)), max (succ (max u1 u2)) (succ (max (max u1 u3) u2))} (LinearMap.{u4, u4, max u1 u2, max (max u1 u3) u2} S S _inst_5 _inst_5 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) (fun (_x : LinearMap.{u4, u4, max u1 u2, max (max u1 u3) u2} S S _inst_5 _inst_5 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) => (α -> M) -> (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4)) (LinearMap.hasCoeToFun.{u4, u4, max u1 u2, max (max u1 u3) u2} S S (α -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u1, u2} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.Function.module.{u1, u4, u2} α S M _inst_5 _inst_3 _inst_6) (LinearMap.module.{u3, u3, u4, max u1 u3, u2} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.Function.module.{u1, u3, u3} α R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_5))) (Fintype.total.{u1, u2, u3, u4} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)) (Submodule.span.{u3, u2} R M _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u1} M α v))
but is expected to have type
- forall {α : Type.{u2}} {M : Type.{u4}} (R : Type.{u3}) [_inst_1 : Fintype.{u2} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u3, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u1, u4} R S M (SMulZeroClass.toSMul.{u3, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u4} R M (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u4} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u3, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{succ u4} (Submodule.{u3, u4} R M _inst_2 _inst_3 _inst_4) (LinearMap.range.{u3, u3, max u2 u3, u4, max (max u2 u4) u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) v) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (RingHomSurjective.ids.{u3} R _inst_2) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearMap.{u1, u1, max u2 u4, max u4 u2 u3} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u2, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13961 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.module.{u2, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13961 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u2 u3, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u2, max (max u3 u4) u2} S S (α -> M) (LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u2, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.module.{u2, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13961 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u2 u3, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13973 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u2, u4, u3, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)) (Submodule.span.{u3, u4} R M _inst_2 _inst_3 _inst_4 (Set.range.{u4, succ u2} M α v))
+ forall {α : Type.{u2}} {M : Type.{u4}} (R : Type.{u3}) [_inst_1 : Fintype.{u2} α] [_inst_2 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Module.{u3, u4} R M _inst_2 _inst_3] {S : Type.{u1}} [_inst_5 : Semiring.{u1} S] [_inst_6 : Module.{u1, u4} S M _inst_5 _inst_3] [_inst_7 : SMulCommClass.{u3, u1, u4} R S M (SMulZeroClass.toSMul.{u3, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u4} R M (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u4} R M (Semiring.toMonoidWithZero.{u3} R _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u3, u4} R M _inst_2 _inst_3 _inst_4)))) (SMulZeroClass.toSMul.{u1, u4} S M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} S M (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} S M (Semiring.toMonoidWithZero.{u1} S _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} S M _inst_5 _inst_3 _inst_6))))] (v : α -> M), Eq.{succ u4} (Submodule.{u3, u4} R M _inst_2 _inst_3 _inst_4) (LinearMap.range.{u3, u3, max u2 u3, u4, max (max u2 u4) u3} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) v) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (RingHomSurjective.ids.{u3} R _inst_2) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), max (max (succ u3) (succ u4)) (succ u2)} (LinearMap.{u1, u1, max u2 u4, max u4 u2 u3} S S _inst_5 _inst_5 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5)) (α -> M) (LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) (Pi.addCommMonoid.{u2, u4} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13965 : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.module.{u2, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13965 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u2 u3, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7)) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> M) => LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u2, max (max u3 u4) u2} S S (α -> M) (LinearMap.{u3, u3, max u2 u3, u4} R R _inst_2 _inst_2 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) (α -> R) M (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4) _inst_5 _inst_5 (Pi.addCommMonoid.{u2, u4} α (fun (ᾰ : α) => M) (fun (i : α) => _inst_3)) (LinearMap.addCommMonoid.{u3, u3, max u2 u3, u4} R R (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (Pi.module.{u2, u4, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13965 : α) => M) S _inst_5 (fun (i : α) => _inst_3) (fun (i : α) => _inst_6)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u1, max u2 u3, u4} R R S (α -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u2, u3} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)))) _inst_3 (Pi.module.{u2, u3, u3} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.13977 : α) => R) R _inst_2 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2))) (fun (i : α) => Semiring.toModule.{u3} R _inst_2)) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_2)) _inst_5 _inst_6 _inst_7) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_5))) (Fintype.total.{u2, u4, u3, u1} α M R _inst_1 _inst_2 _inst_3 _inst_4 S _inst_5 _inst_6 _inst_7) v)) (Submodule.span.{u3, u4} R M _inst_2 _inst_3 _inst_4 (Set.range.{u4, succ u2} M α v))
Case conversion may be inaccurate. Consider using '#align fintype.range_total Fintype.range_totalₓ'. -/
@[simp]
theorem Fintype.range_total : (Fintype.total R S v).range = Submodule.span R (Set.range v) := by
@@ -2055,7 +2055,7 @@ theorem splittingOfFinsuppSurjective_injective (f : M →ₗ[R] α →₀ R) (s
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3)
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16530 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u1) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16530 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16530 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16530 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16544 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) _inst_3)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16534 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))), (Function.Surjective.{succ u2, max (succ u1) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearMap.{u1, u1, u2, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16534 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16534 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16534 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (LinearMap.{u1, u1, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.module.{u3, u1, u1} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16548 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : α) => Semiring.toModule.{u1} R _inst_1)) _inst_3)
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective LinearMap.splittingOfFunOnFintypeSurjectiveₓ'. -/
-- See also `linear_map.splitting_of_finsupp_surjective`
/-- A surjective linear map to functions on a finite type has a splitting. -/
@@ -2069,7 +2069,7 @@ def splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R) (s
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Eq.{succ (max u3 u1)} (LinearMap.{u1, u1, max u3 u1, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (LinearMap.comp.{u1, u1, u1, max u3 u1, u2, max u3 u1} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomCompTriple.right_ids.{u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u1, max u3 u1} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16610 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), 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α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16610 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Eq.{max (succ u2) (succ u3)} (LinearMap.{u2, u2, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16544 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16610 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.comp.{u2, u2, u2, max u2 u3, u1, max u2 u3} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16544 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16610 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u2, max u2 u3} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16544 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16614 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16614 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16614 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16614 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Eq.{max (succ u2) (succ u3)} (LinearMap.{u2, u2, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) (α -> R) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16548 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16614 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.comp.{u2, u2, u2, max u2 u3, u1, max u2 u3} R R R (α -> R) M (α -> R) _inst_1 _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16548 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16614 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s)) (LinearMap.id.{u2, max u2 u3} R (α -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16548 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)))
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective_splits LinearMap.splittingOfFunOnFintypeSurjective_splitsₓ'. -/
theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : f.comp (splittingOfFunOnFintypeSurjective f s) = LinearMap.id :=
@@ -2085,7 +2085,7 @@ theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R]
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Function.LeftInverse.{max (succ u3) (succ u1), succ u2} (α -> R) M (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f) (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) (fun (_x : LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) => (α -> R) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, u2} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16740 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16544 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16544 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => 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+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16744 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), 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α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16744 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Function.LeftInverse.{max (succ u2) (succ u3), succ u1} (α -> R) M (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16744 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16548 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16548 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => 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Case conversion may be inaccurate. Consider using '#align linear_map.left_inverse_splitting_of_fun_on_fintype_surjective LinearMap.leftInverse_splittingOfFunOnFintypeSurjectiveₓ'. -/
theorem leftInverse_splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : LeftInverse f (splittingOfFunOnFintypeSurjective f s) := fun g =>
@@ -2096,7 +2096,7 @@ theorem leftInverse_splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (s : Function.Surjective.{succ u2, max (succ u3) (succ u1)} M (α -> R) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => M -> α -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)), Function.Injective.{max (succ u3) (succ u1), succ u2} (α -> R) M (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) (fun (_x : LinearMap.{u1, u1, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3) => (α -> R) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, u2} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u1} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Pi.Function.module.{u3, u1, u1} α R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16796 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16796 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16796 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16796 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Function.Injective.{max (succ u2) (succ u3), succ u1} (α -> R) M (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16544 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16544 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16544 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {α : Type.{u3}} [_inst_6 : Fintype.{u3} α] (f : LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16800 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) (s : Function.Surjective.{succ u1, max (succ u2) (succ u3)} M (α -> R) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, max (succ u2) (succ u3)} (LinearMap.{u2, u2, u1, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M (α -> R) _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16800 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16800 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => α -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u2 u3} R R M (α -> R) _inst_1 _inst_1 _inst_2 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16800 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)), Function.Injective.{max (succ u2) (succ u3), succ u1} (α -> R) M (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (α -> R) M (Pi.addCommMonoid.{u3, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16548 : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16548 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3) (α -> R) (fun (_x : α -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : α -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (α -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} α (fun (ᾰ : α) => R) (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} α (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.16548 : α) => R) R _inst_1 (fun (i : α) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : α) => Semiring.toModule.{u2} R _inst_1)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.splittingOfFunOnFintypeSurjective.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 α _inst_6 f s))
Case conversion may be inaccurate. Consider using '#align linear_map.splitting_of_fun_on_fintype_surjective_injective LinearMap.splittingOfFunOnFintypeSurjective_injectiveₓ'. -/
theorem splittingOfFunOnFintypeSurjective_injective [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : Injective (splittingOfFunOnFintypeSurjective f s) :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442
@@ -326,7 +326,7 @@ lean 3 declaration is
but is expected to have type
forall {α : Type.{u3}} {M : Type.{u2}} (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {s : Set.{u3} α} (p : Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))), Iff (Membership.mem.{max u3 u2, max u2 u3} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Submodule.instSetLikeSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4))) p (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s)) (forall (x : α), (Not (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) x s)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) x) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) α (fun (_x : α) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) _x) (Finsupp.funLike.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) p x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) x) (AddMonoid.toZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) x) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : α) => M) x) _inst_3))))))
Case conversion may be inaccurate. Consider using '#align finsupp.mem_supported' Finsupp.mem_supported'ₓ'. -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ∉ » s) -/
theorem mem_supported' {s : Set α} (p : α →₀ M) :
p ∈ supported M R s ↔ ∀ (x) (_ : x ∉ s), p x = 0 := by
haveI := Classical.decPred fun x : α => x ∈ s <;>
@@ -788,7 +788,7 @@ lean 3 declaration is
but is expected to have type
forall {α : Type.{u4}} (M : Type.{u2}) (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {α' : Type.{u3}} (f : α -> α') {s : Set.{u4} α}, (forall (a : α), (Membership.mem.{u4, u4} α (Set.{u4} α) (Set.instMembershipSet.{u4} α) a s) -> (forall (b : α), (Membership.mem.{u4, u4} α (Set.{u4} α) (Set.instMembershipSet.{u4} α) b s) -> (Eq.{succ u3} α' (f a) (f b)) -> (Eq.{succ u4} α a b))) -> (Disjoint.{max u2 u4} (Submodule.{u1, max u2 u4} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (OmegaCompletePartialOrder.toPartialOrder.{max u4 u2} (Submodule.{u1, max u2 u4} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.instOmegaCompletePartialOrder.{max u4 u2} (Submodule.{u1, max u2 u4} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u4 u2} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4)))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u1, max u4 u2} R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) (LinearMap.ker.{u1, u1, max u4 u2, max u2 u3, max (max u2 u3) u4} R R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α' M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u4, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α' M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α' M R _inst_1 _inst_3 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u4 u2, max u2 u3} R R (Finsupp.{u4, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) (Finsupp.{u3, u2} α' M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 _inst_1 (Finsupp.addCommMonoid.{u4, u2} α M _inst_3) (Finsupp.addCommMonoid.{u3, u2} α' M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u4, u2, u1} α M R _inst_1 _inst_3 _inst_4) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α' M R _inst_1 _inst_3 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.lmapDomain.{u4, u2, u1, u3} α M R _inst_1 _inst_3 _inst_4 α' f)))
Case conversion may be inaccurate. Consider using '#align finsupp.lmap_domain_disjoint_ker Finsupp.lmapDomain_disjoint_kerₓ'. -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (a b «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a b «expr ∈ » s) -/
theorem lmapDomain_disjoint_ker (f : α → α') {s : Set α}
(H : ∀ (a) (_ : a ∈ s) (b) (_ : b ∈ s), f a = f b → a = b) :
Disjoint (supported M R s) (lmapDomain M R f).ker :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211
@@ -492,9 +492,9 @@ theorem supported_unionᵢ {δ : Type _} (s : δ → Set α) :
/- warning: finsupp.supported_union -> Finsupp.supported_union is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α) (t : Set.{u1} α), Eq.{succ (max u1 u2)} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) (HasSup.sup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SemilatticeSup.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Lattice.toSemilatticeSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))))) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 t))
+ forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α) (t : Set.{u1} α), Eq.{succ (max u1 u2)} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) (Sup.sup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (SemilatticeSup.toHasSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Lattice.toSemilatticeSup.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)))))) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 t))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (t : Set.{u3} α), Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (Union.union.{u3} (Set.{u3} α) (Set.instUnionSet.{u3} α) s t)) (HasSup.sup.{max u2 u3} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SemilatticeSup.toHasSup.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Lattice.toSemilatticeSup.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toLattice.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))))) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 t))
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (t : Set.{u3} α), Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (Union.union.{u3} (Set.{u3} α) (Set.instUnionSet.{u3} α) s t)) (Sup.sup.{max u2 u3} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (SemilatticeSup.toSup.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Lattice.toSemilatticeSup.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (ConditionallyCompleteLattice.toLattice.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.completeLattice.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)))))) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 t))
Case conversion may be inaccurate. Consider using '#align finsupp.supported_union Finsupp.supported_unionₓ'. -/
theorem supported_union (s t : Set α) : supported M R (s ∪ t) = supported M R s ⊔ supported M R t :=
by erw [Set.union_eq_unionᵢ, supported_Union, supᵢ_bool_eq] <;> rfl
@@ -513,9 +513,9 @@ theorem supported_interᵢ {ι : Type _} (s : ι → Set α) :
/- warning: finsupp.supported_inter -> Finsupp.supported_inter is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α) (t : Set.{u1} α), Eq.{succ (max u1 u2)} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)) (HasInf.inf.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasInf.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 t))
+ forall {α : Type.{u1}} {M : Type.{u2}} {R : Type.{u3}} [_inst_1 : Semiring.{u3} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_3] (s : Set.{u1} α) (t : Set.{u1} α), Eq.{succ (max u1 u2)} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)) (Inf.inf.{max u1 u2} (Submodule.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Submodule.hasInf.{u3, max u1 u2} R (Finsupp.{u1, u2} α M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} α M _inst_3) (Finsupp.module.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 s) (Finsupp.supported.{u1, u2, u3} α M R _inst_1 _inst_3 _inst_4 t))
but is expected to have type
- forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (t : Set.{u3} α), Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (Inter.inter.{u3} (Set.{u3} α) (Set.instInterSet.{u3} α) s t)) (HasInf.inf.{max u2 u3} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instHasInfSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 t))
+ forall {α : Type.{u3}} {M : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (s : Set.{u3} α) (t : Set.{u3} α), Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 (Inter.inter.{u3} (Set.{u3} α) (Set.instInterSet.{u3} α) s t)) (Inf.inf.{max u2 u3} (Submodule.{u1, max u2 u3} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Submodule.instInfSubmodule.{u1, max u3 u2} R (Finsupp.{u3, u2} α M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} α M _inst_3) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4)) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 s) (Finsupp.supported.{u3, u2, u1} α M R _inst_1 _inst_3 _inst_4 t))
Case conversion may be inaccurate. Consider using '#align finsupp.supported_inter Finsupp.supported_interₓ'. -/
theorem supported_inter (s t : Set α) : supported M R (s ∩ t) = supported M R s ⊓ supported M R t :=
by rw [Set.inter_eq_interᵢ, supported_Inter, infᵢ_bool_eq] <;> rfl
mathlib commit https://github.com/leanprover-community/mathlib/commit/3ade05ac9447ae31a22d2ea5423435e054131240
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
! This file was ported from Lean 3 source module linear_algebra.finsupp
-! leanprover-community/mathlib commit 565eb991e264d0db702722b4bde52ee5173c9950
+! leanprover-community/mathlib commit 23aa88e32dcc9d2a24cca7bc23268567ed4cd7d6
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -15,6 +15,9 @@ import Mathbin.LinearAlgebra.Span
/-!
# Properties of the module `α →₀ M`
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
Given an `R`-module `M`, the `R`-module structure on `α →₀ M` is defined in
`data.finsupp.basic`.
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
Empty lines were removed by executing the following Python script twice
import os
import re
# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
for filename in files:
if filename.endswith('.lean'):
file_path = os.path.join(dir_path, filename)
# Open the file and read its contents
with open(file_path, 'r') as file:
content = file.read()
# Use a regular expression to replace sequences of "variable" lines separated by empty lines
# with sequences without empty lines
modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)
# Write the modified content back to the file
with open(file_path, 'w') as file:
file.write(modified_content)
@@ -1087,7 +1087,6 @@ end Sum
section Sigma
variable {η : Type*} [Fintype η] {ιs : η → Type*} [Zero α]
-
variable (R)
/-- On a `Fintype η`, `Finsupp.split` is a linear equivalence between
@@ -1162,9 +1161,7 @@ end Finsupp
section Fintype
variable {α M : Type*} (R : Type*) [Fintype α] [Semiring R] [AddCommMonoid M] [Module R M]
-
variable (S : Type*) [Semiring S] [Module S M] [SMulCommClass R S M]
-
variable (v : α → M)
/-- `Fintype.total R S v f` is the linear combination of vectors in `v` with weights in `f`.
@@ -1249,7 +1246,6 @@ end SpanRange
end Fintype
variable {R : Type*} {M : Type*} {N : Type*}
-
variable [Semiring R] [AddCommMonoid M] [Module R M] [AddCommMonoid N] [Module R N]
section
Finsupp.filter
computable (#8979)
This doesn't have any significant downstream fallout, and removes some subsingleton elimination from one or two proofs.
This enables some trivial computations on factorizations, eg finding the odd prime factors:
/-- info: fun₀ | 3 => 2 | 5 => 1 -/
#guard_msgs in
#eval (Nat.factorization 720).filter Odd
@@ -344,7 +344,7 @@ theorem supported_eq_span_single (s : Set α) :
variable (M)
/-- Interpret `Finsupp.filter s` as a linear map from `α →₀ M` to `supported M R s`. -/
-def restrictDom (s : Set α) : (α →₀ M) →ₗ[R] supported M R s :=
+def restrictDom (s : Set α) [DecidablePred (· ∈ s)] : (α →₀ M) →ₗ[R] supported M R s :=
LinearMap.codRestrict _
{ toFun := filter (· ∈ s)
map_add' := fun _ _ => filter_add
@@ -357,21 +357,21 @@ variable {M R}
section
@[simp]
-theorem restrictDom_apply (s : Set α) (l : α →₀ M) :
- ((restrictDom M R s : (α →₀ M) →ₗ[R] supported M R s) l : α →₀ M) = Finsupp.filter (· ∈ s) l :=
- rfl
+theorem restrictDom_apply (s : Set α) (l : α →₀ M) [DecidablePred (· ∈ s)]:
+ (restrictDom M R s l : α →₀ M) = Finsupp.filter (· ∈ s) l := rfl
#align finsupp.restrict_dom_apply Finsupp.restrictDom_apply
end
-theorem restrictDom_comp_subtype (s : Set α) :
+theorem restrictDom_comp_subtype (s : Set α) [DecidablePred (· ∈ s)] :
(restrictDom M R s).comp (Submodule.subtype _) = LinearMap.id := by
ext l a
by_cases h : a ∈ s <;> simp [h]
exact ((mem_supported' R l.1).1 l.2 a h).symm
#align finsupp.restrict_dom_comp_subtype Finsupp.restrictDom_comp_subtype
-theorem range_restrictDom (s : Set α) : LinearMap.range (restrictDom M R s) = ⊤ :=
+theorem range_restrictDom (s : Set α) [DecidablePred (· ∈ s)] :
+ LinearMap.range (restrictDom M R s) = ⊤ :=
range_eq_top.2 <|
Function.RightInverse.surjective <| LinearMap.congr_fun (restrictDom_comp_subtype s)
#align finsupp.range_restrict_dom Finsupp.range_restrictDom
refine
s (#10762)
I replaced a few "terminal" refine/refine'
s with exact
.
The strategy was very simple-minded: essentially any refine
whose following line had smaller indentation got replaced by exact
and then I cleaned up the mess.
This PR certainly leaves some further terminal refine
s, but maybe the current change is beneficial.
@@ -333,7 +333,7 @@ theorem supported_eq_span_single (s : Set α) :
· rintro _ ⟨_, hp, rfl⟩
exact single_mem_supported R 1 hp
· rw [← l.sum_single]
- refine' sum_mem fun i il => _
+ refine sum_mem fun i il => ?_
-- Porting note: Needed to help this convert quite a bit replacing underscores
convert smul_mem (M := α →₀ R) (x := single i 1) (span R ((fun i => single i 1) '' s)) (l i) ?_
· simp [span]
@@ -916,7 +916,7 @@ theorem domLCongr_symm {α₁ α₂ : Type*} (f : α₁ ≃ α₂) :
LinearEquiv.ext fun _ => rfl
#align finsupp.dom_lcongr_symm Finsupp.domLCongr_symm
--- @[simp] -- Porting note: simp can prove this
+-- @[simp] -- Porting note (#10618): simp can prove this
theorem domLCongr_single {α₁ : Type*} {α₂ : Type*} (e : α₁ ≃ α₂) (i : α₁) (m : M) :
(Finsupp.domLCongr e : _ ≃ₗ[R] _) (Finsupp.single i m) = Finsupp.single (e i) m := by
simp
@@ -1407,13 +1407,13 @@ theorem splittingOfFinsuppSurjective_injective (f : M →ₗ[R] α →₀ R) (s
-- See also `LinearMap.splittingOfFinsuppSurjective`
/-- A surjective linear map to functions on a finite type has a splitting. -/
-def splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R) (s : Surjective f) :
+def splittingOfFunOnFintypeSurjective [Finite α] (f : M →ₗ[R] α → R) (s : Surjective f) :
(α → R) →ₗ[R] M :=
(Finsupp.lift _ _ _ fun x : α => (s (Finsupp.single x 1)).choose).comp
(linearEquivFunOnFinite R R α).symm.toLinearMap
#align linear_map.splitting_of_fun_on_fintype_surjective LinearMap.splittingOfFunOnFintypeSurjective
-theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R] α → R)
+theorem splittingOfFunOnFintypeSurjective_splits [Finite α] (f : M →ₗ[R] α → R)
(s : Surjective f) : f.comp (splittingOfFunOnFintypeSurjective f s) = LinearMap.id := by
classical
-- Porting note: `ext` can't find appropriate theorems.
@@ -1424,12 +1424,12 @@ theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R]
rw [zero_smul]
#align linear_map.splitting_of_fun_on_fintype_surjective_splits LinearMap.splittingOfFunOnFintypeSurjective_splits
-theorem leftInverse_splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R)
+theorem leftInverse_splittingOfFunOnFintypeSurjective [Finite α] (f : M →ₗ[R] α → R)
(s : Surjective f) : LeftInverse f (splittingOfFunOnFintypeSurjective f s) := fun g =>
LinearMap.congr_fun (splittingOfFunOnFintypeSurjective_splits f s) g
#align linear_map.left_inverse_splitting_of_fun_on_fintype_surjective LinearMap.leftInverse_splittingOfFunOnFintypeSurjective
-theorem splittingOfFunOnFintypeSurjective_injective [Fintype α] (f : M →ₗ[R] α → R)
+theorem splittingOfFunOnFintypeSurjective_injective [Finite α] (f : M →ₗ[R] α → R)
(s : Surjective f) : Injective (splittingOfFunOnFintypeSurjective f s) :=
(leftInverse_splittingOfFunOnFintypeSurjective f s).injective
#align linear_map.splitting_of_fun_on_fintype_surjective_injective LinearMap.splittingOfFunOnFintypeSurjective_injective
@@ -6,6 +6,7 @@ Authors: Johannes Hölzl
import Mathlib.Data.Finsupp.Encodable
import Mathlib.LinearAlgebra.Pi
import Mathlib.LinearAlgebra.Span
+import Mathlib.Data.Set.Countable
#align_import linear_algebra.finsupp from "leanprover-community/mathlib"@"9d684a893c52e1d6692a504a118bfccbae04feeb"
Basis.smul
(#9382)
Add various LinearMap.CompatibleSMul
instances that ultimately lead to generalization of Basis.smul
to allow a noncommutative base ring. The key observations that allows the generalization are IsScalarTower.smulHomClass
and isScalarTower_of_injective
.
Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>
@@ -170,6 +170,24 @@ def lapply (a : α) : (α →₀ M) →ₗ[R] M :=
{ Finsupp.applyAddHom a with map_smul' := fun _ _ => rfl }
#align finsupp.lapply Finsupp.lapply
+section CompatibleSMul
+
+variable (R S M N ι : Type*)
+variable [Semiring S] [AddCommMonoid M] [AddCommMonoid N] [Module S M] [Module S N]
+
+instance _root_.LinearMap.CompatibleSMul.finsupp_dom [SMulZeroClass R M] [DistribSMul R N]
+ [LinearMap.CompatibleSMul M N R S] : LinearMap.CompatibleSMul (ι →₀ M) N R S where
+ map_smul f r m := by
+ conv_rhs => rw [← sum_single m, map_finsupp_sum, smul_sum]
+ erw [← sum_single (r • m), sum_mapRange_index single_zero, map_finsupp_sum]
+ congr; ext i m; exact (f.comp <| lsingle i).map_smul_of_tower r m
+
+instance _root_.LinearMap.CompatibleSMul.finsupp_cod [SMul R M] [SMulZeroClass R N]
+ [LinearMap.CompatibleSMul M N R S] : LinearMap.CompatibleSMul M (ι →₀ N) R S where
+ map_smul f r m := by ext i; apply ((lapply i).comp f).map_smul_of_tower
+
+end CompatibleSMul
+
/-- Forget that a function is finitely supported.
This is the linear version of `Finsupp.toFun`. -/
@@ -295,7 +295,7 @@ theorem mem_supported {s : Set α} (p : α →₀ M) : p ∈ supported M R s ↔
#align finsupp.mem_supported Finsupp.mem_supported
theorem mem_supported' {s : Set α} (p : α →₀ M) :
- p ∈ supported M R s ↔ ∀ (x) (_ : x ∉ s), p x = 0 := by
+ p ∈ supported M R s ↔ ∀ x ∉ s, p x = 0 := by
haveI := Classical.decPred fun x : α => x ∈ s; simp [mem_supported, Set.subset_def, not_imp_comm]
#align finsupp.mem_supported' Finsupp.mem_supported'
@@ -590,7 +590,7 @@ theorem lmapDomain_supported (f : α → α') (s : Set α) :
#align finsupp.lmap_domain_supported Finsupp.lmapDomain_supported
theorem lmapDomain_disjoint_ker (f : α → α') {s : Set α}
- (H : ∀ (a) (_ : a ∈ s) (b) (_ : b ∈ s), f a = f b → a = b) :
+ (H : ∀ a ∈ s, ∀ b ∈ s, f a = f b → a = b) :
Disjoint (supported M R s) (ker (lmapDomain M R f)) := by
rw [disjoint_iff_inf_le]
rintro l ⟨h₁, h₂⟩
Finsupp
instance (#8868)
The original Coalgebra R (ι →₀ R)
is now recovered from [Coalgebra R A] : Coalgebra R (ι →₀ A)
as a special case.
Salvaged from https://github.com/leanprover-community/mathlib4/pull/8621#discussion_r1408532458
@@ -213,6 +213,13 @@ theorem lapply_apply (a : α) (f : α →₀ M) : (lapply a : (α →₀ M) →
rfl
#align finsupp.lapply_apply Finsupp.lapply_apply
+@[simp]
+theorem lapply_comp_lsingle_same (a : α) : lapply a ∘ₗ lsingle a = (.id : M →ₗ[R] M) := by ext; simp
+
+@[simp]
+theorem lapply_comp_lsingle_of_ne (a a' : α) (h : a ≠ a') :
+ lapply a ∘ₗ lsingle a' = (0 : M →ₗ[R] M) := by ext; simp [h.symm]
+
@[simp]
theorem ker_lsingle (a : α) : ker (lsingle a : M →ₗ[R] α →₀ M) = ⊥ :=
ker_eq_bot_of_injective (single_injective a)
@@ -467,6 +474,9 @@ theorem lsum_single (f : α → M →ₗ[R] N) (i : α) (m : M) :
Finsupp.sum_single_index (f i).map_zero
#align finsupp.lsum_single Finsupp.lsum_single
+@[simp] theorem lsum_comp_lsingle (f : α → M →ₗ[R] N) (i : α) :
+ Finsupp.lsum S f ∘ₗ lsingle i = f i := by ext; simp
+
theorem lsum_symm_apply (f : (α →₀ M) →ₗ[R] N) (x : α) : (lsum S).symm f x = f.comp (lsingle x) :=
rfl
#align finsupp.lsum_symm_apply Finsupp.lsum_symm_apply
@@ -826,7 +826,7 @@ variable {α} {M} {v}
theorem totalOn_range (s : Set α) : LinearMap.range (Finsupp.totalOn α M R v s) = ⊤ := by
rw [Finsupp.totalOn, LinearMap.range_eq_map, LinearMap.map_codRestrict,
- ←LinearMap.range_le_iff_comap, range_subtype, Submodule.map_top, LinearMap.range_comp,
+ ← LinearMap.range_le_iff_comap, range_subtype, Submodule.map_top, LinearMap.range_comp,
range_subtype]
exact (span_image_eq_map_total _ _).le
#align finsupp.total_on_range Finsupp.totalOn_range
This reduces the file from ~2600 lines to ~1600 lines.
Co-authored-by: Vierkantor <vierkantor@vierkantor.com> Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com>
@@ -50,6 +50,94 @@ open BigOperators
namespace Finsupp
+section SMul
+
+variable {α : Type*} {β : Type*} {R : Type*} {M : Type*} {M₂ : Type*}
+
+theorem smul_sum [Zero β] [AddCommMonoid M] [DistribSMul R M] {v : α →₀ β} {c : R} {h : α → β → M} :
+ c • v.sum h = v.sum fun a b => c • h a b :=
+ Finset.smul_sum
+#align finsupp.smul_sum Finsupp.smul_sum
+
+@[simp]
+theorem sum_smul_index_linearMap' [Semiring R] [AddCommMonoid M] [Module R M] [AddCommMonoid M₂]
+ [Module R M₂] {v : α →₀ M} {c : R} {h : α → M →ₗ[R] M₂} :
+ ((c • v).sum fun a => h a) = c • v.sum fun a => h a := by
+ rw [Finsupp.sum_smul_index', Finsupp.smul_sum]
+ · simp only [map_smul]
+ · intro i
+ exact (h i).map_zero
+#align finsupp.sum_smul_index_linear_map' Finsupp.sum_smul_index_linearMap'
+
+end SMul
+
+section LinearEquivFunOnFinite
+
+variable (R : Type*) {S : Type*} (M : Type*) (α : Type*)
+variable [Finite α] [AddCommMonoid M] [Semiring R] [Module R M]
+
+/-- Given `Finite α`, `linearEquivFunOnFinite R` is the natural `R`-linear equivalence between
+`α →₀ β` and `α → β`. -/
+@[simps apply]
+noncomputable def linearEquivFunOnFinite : (α →₀ M) ≃ₗ[R] α → M :=
+ { equivFunOnFinite with
+ toFun := (⇑)
+ map_add' := fun _ _ => rfl
+ map_smul' := fun _ _ => rfl }
+#align finsupp.linear_equiv_fun_on_finite Finsupp.linearEquivFunOnFinite
+
+@[simp]
+theorem linearEquivFunOnFinite_single [DecidableEq α] (x : α) (m : M) :
+ (linearEquivFunOnFinite R M α) (single x m) = Pi.single x m :=
+ equivFunOnFinite_single x m
+#align finsupp.linear_equiv_fun_on_finite_single Finsupp.linearEquivFunOnFinite_single
+
+@[simp]
+theorem linearEquivFunOnFinite_symm_single [DecidableEq α] (x : α) (m : M) :
+ (linearEquivFunOnFinite R M α).symm (Pi.single x m) = single x m :=
+ equivFunOnFinite_symm_single x m
+#align finsupp.linear_equiv_fun_on_finite_symm_single Finsupp.linearEquivFunOnFinite_symm_single
+
+@[simp]
+theorem linearEquivFunOnFinite_symm_coe (f : α →₀ M) : (linearEquivFunOnFinite R M α).symm f = f :=
+ (linearEquivFunOnFinite R M α).symm_apply_apply f
+#align finsupp.linear_equiv_fun_on_finite_symm_coe Finsupp.linearEquivFunOnFinite_symm_coe
+
+end LinearEquivFunOnFinite
+
+section LinearEquiv.finsuppUnique
+
+variable (R : Type*) {S : Type*} (M : Type*)
+variable [AddCommMonoid M] [Semiring R] [Module R M]
+variable (α : Type*) [Unique α]
+
+/-- If `α` has a unique term, then the type of finitely supported functions `α →₀ M` is
+`R`-linearly equivalent to `M`. -/
+noncomputable def LinearEquiv.finsuppUnique : (α →₀ M) ≃ₗ[R] M :=
+ { Finsupp.equivFunOnFinite.trans (Equiv.funUnique α M) with
+ map_add' := fun _ _ => rfl
+ map_smul' := fun _ _ => rfl }
+#align finsupp.linear_equiv.finsupp_unique Finsupp.LinearEquiv.finsuppUnique
+
+variable {R M}
+
+@[simp]
+theorem LinearEquiv.finsuppUnique_apply (f : α →₀ M) :
+ LinearEquiv.finsuppUnique R M α f = f default :=
+ rfl
+#align finsupp.linear_equiv.finsupp_unique_apply Finsupp.LinearEquiv.finsuppUnique_apply
+
+variable {α}
+
+@[simp]
+theorem LinearEquiv.finsuppUnique_symm_apply [Unique α] (m : M) :
+ (LinearEquiv.finsuppUnique R M α).symm m = Finsupp.single default m := by
+ ext; simp [LinearEquiv.finsuppUnique, Equiv.funUnique, single, Pi.single,
+ equivFunOnFinite, Function.update]
+#align finsupp.linear_equiv.finsupp_unique_symm_apply Finsupp.LinearEquiv.finsuppUnique_symm_apply
+
+end LinearEquiv.finsuppUnique
+
variable {α : Type*} {M : Type*} {N : Type*} {P : Type*} {R : Type*} {S : Type*}
variable [Semiring R] [Semiring S] [AddCommMonoid M] [Module R M]
variable [AddCommMonoid N] [Module R N]
@@ -1318,3 +1406,33 @@ theorem splittingOfFunOnFintypeSurjective_injective [Fintype α] (f : M →ₗ[R
#align linear_map.splitting_of_fun_on_fintype_surjective_injective LinearMap.splittingOfFunOnFintypeSurjective_injective
end LinearMap
+
+namespace LinearMap
+
+section AddCommMonoid
+
+variable {R : Type*} {R₂ : Type*} {M : Type*} {M₂ : Type*} {ι : Type*}
+variable [Semiring R] [Semiring R₂] [AddCommMonoid M] [AddCommMonoid M₂] {σ₁₂ : R →+* R₂}
+variable [Module R M] [Module R₂ M₂]
+variable {γ : Type*} [Zero γ]
+
+section Finsupp
+
+#align linear_map.map_finsupp_sum map_finsupp_sumₓ
+#align linear_equiv.map_finsupp_sum map_finsupp_sumₓ
+
+theorem coe_finsupp_sum (t : ι →₀ γ) (g : ι → γ → M →ₛₗ[σ₁₂] M₂) :
+ ⇑(t.sum g) = t.sum fun i d => g i d := rfl
+#align linear_map.coe_finsupp_sum LinearMap.coe_finsupp_sum
+
+@[simp]
+theorem finsupp_sum_apply (t : ι →₀ γ) (g : ι → γ → M →ₛₗ[σ₁₂] M₂) (b : M) :
+ (t.sum g) b = t.sum fun i d => g i d b :=
+ sum_apply _ _ _
+#align linear_map.finsupp_sum_apply LinearMap.finsupp_sum_apply
+
+end Finsupp
+
+end AddCommMonoid
+
+end LinearMap
Removes nonterminal simps on lines looking like simp [...]
@@ -1114,7 +1114,7 @@ theorem mem_span_range_iff_exists_fun :
x ∈ span R (range v) ↔ ∃ c : α → R, ∑ i, c i • v i = x := by
-- Porting note: `Finsupp.equivFunOnFinite.surjective.exists` should be come before `simp`.
rw [Finsupp.equivFunOnFinite.surjective.exists]
- simp [Finsupp.mem_span_range_iff_exists_finsupp, Finsupp.equivFunOnFinite_apply]
+ simp only [Finsupp.mem_span_range_iff_exists_finsupp, Finsupp.equivFunOnFinite_apply]
exact exists_congr fun c => Eq.congr_left <| Finsupp.sum_fintype _ _ fun i => zero_smul _ _
#align mem_span_range_iff_exists_fun mem_span_range_iff_exists_fun
Sup
and sSup
of LieSubmodule
s (#7608)
The point is that the following four lemmas are now all true by definition:
LieSubmodule.inf_coe_toSubmodule
LieSubmodule.sInf_coe_toSubmodule
LieSubmodule.sup_coe_toSubmodule
[previously existed but not true by definition]LieSubmodule.sSup_coe_toSubmodule
[previously did not exist]@@ -1182,6 +1182,17 @@ theorem Submodule.mem_iSup_iff_exists_finset {ι : Sort _} {p : ι → Submodule
iSup_mono (fun i => (iSup_const_le : _ ≤ p i)) hs⟩
#align submodule.mem_supr_iff_exists_finset Submodule.mem_iSup_iff_exists_finset
+theorem Submodule.mem_sSup_iff_exists_finset {S : Set (Submodule R M)} {m : M} :
+ m ∈ sSup S ↔ ∃ s : Finset (Submodule R M), ↑s ⊆ S ∧ m ∈ ⨆ i ∈ s, i := by
+ rw [sSup_eq_iSup, iSup_subtype', Submodule.mem_iSup_iff_exists_finset]
+ refine ⟨fun ⟨s, hs⟩ ↦ ⟨s.map (Function.Embedding.subtype S), ?_, ?_⟩,
+ fun ⟨s, hsS, hs⟩ ↦ ⟨s.preimage (↑) (Subtype.coe_injective.injOn _), ?_⟩⟩
+ · simpa using fun x _ ↦ x.property
+ · suffices m ∈ ⨆ (i) (hi : i ∈ S) (_ : ⟨i, hi⟩ ∈ s), i by simpa
+ rwa [iSup_subtype']
+ · have : ⨆ (i) (_ : i ∈ S ∧ i ∈ s), i = ⨆ (i) (_ : i ∈ s), i := by convert rfl; aesop
+ simpa only [Finset.mem_preimage, iSup_subtype, iSup_and', this]
+
theorem mem_span_finset {s : Finset M} {x : M} :
x ∈ span R (↑s : Set M) ↔ ∃ f : M → R, ∑ i in s, f i • i = x :=
⟨fun hx =>
In several places, we unfold Finsupp.sum
just to use Finset.sum_eq_single
; this adds the missing lemma.
@@ -503,10 +503,11 @@ theorem lmapDomain_disjoint_ker (f : α → α') {s : Set α}
· have : Finsupp.sum l (fun a => Finsupp.single (f a)) (f x) = 0 := by
rw [h₂]
rfl
- rw [Finsupp.sum_apply, Finsupp.sum, Finset.sum_eq_single x, single_eq_same] at this
+ rw [Finsupp.sum_apply, Finsupp.sum_eq_single x, single_eq_same] at this
· simpa
· intro y hy xy
- simp [mt (H _ (h₁ hy) _ xs) xy]
+ simp only [SetLike.mem_coe, mem_supported, subset_def, Finset.mem_coe, mem_support_iff] at h₁
+ simp [mt (H _ (h₁ _ hy) _ xs) xy]
· simp (config := { contextual := true })
· by_contra h
exact xs (h₁ <| Finsupp.mem_support_iff.2 h)
@@ -471,10 +471,11 @@ theorem supported_comap_lmapDomain (f : α → α') (s : Set α') :
exact Set.Subset.trans mapDomain_support hl
#align finsupp.supported_comap_lmap_domain Finsupp.supported_comap_lmapDomain
-theorem lmapDomain_supported [Nonempty α] (f : α → α') (s : Set α) :
+theorem lmapDomain_supported (f : α → α') (s : Set α) :
(supported M R s).map (lmapDomain M R f) = supported M R (f '' s) := by
classical
- inhabit α
+ cases isEmpty_or_nonempty α
+ · simp [s.eq_empty_of_isEmpty]
refine
le_antisymm
(map_le_iff_le_comap.2 <|
@@ -823,7 +823,7 @@ def mapRange.linearMap (f : M →ₗ[R] N) : (α →₀ M) →ₗ[R] α →₀ N
-- Porting note: This was generated by `simps!`.
@[simp]
theorem mapRange.linearMap_apply (f : M →ₗ[R] N) (g : α →₀ M) :
- mapRange.linearMap f g = mapRange f f.map_zero g := rfl
+ mapRange.linearMap f g = mapRange f f.map_zero g := rfl
#align finsupp.map_range.linear_map_apply Finsupp.mapRange.linearMap_apply
@[simp]
_root_.map_sum
more consistently (#7189)
Also _root_.map_smul
when in the neighbourhood.
@@ -1161,7 +1161,7 @@ protected theorem Submodule.finsupp_sum_mem {ι β : Type*} [Zero β] (S : Submo
theorem LinearMap.map_finsupp_total (f : M →ₗ[R] N) {ι : Type*} {g : ι → M} (l : ι →₀ R) :
f (Finsupp.total ι M R g l) = Finsupp.total ι N R (f ∘ g) l := by
-- Porting note: `(· ∘ ·)` is required.
- simp only [Finsupp.total_apply, Finsupp.total_apply, Finsupp.sum, f.map_sum, f.map_smul, (· ∘ ·)]
+ simp only [Finsupp.total_apply, Finsupp.total_apply, Finsupp.sum, map_sum, map_smul, (· ∘ ·)]
#align linear_map.map_finsupp_total LinearMap.map_finsupp_total
theorem Submodule.exists_finset_of_mem_iSup {ι : Sort _} (p : ι → Submodule R M) {m : M}
@@ -1200,6 +1200,34 @@ theorem mem_span_set {m : M} {s : Set M} :
exact Finsupp.mem_span_image_iff_total R (v := _root_.id (α := M))
#align mem_span_set mem_span_set
+/-- An element `m ∈ M` is contained in the `R`-submodule spanned by a set `s ⊆ M`, if and only if
+`m` can be written as a finite `R`-linear combination of elements of `s`.
+The implementation uses a sum indexed by `Fin n` for some `n`. -/
+lemma mem_span_set' {m : M} {s : Set M} :
+ m ∈ Submodule.span R s ↔ ∃ (n : ℕ) (f : Fin n → R) (g : Fin n → s),
+ ∑ i, f i • (g i : M) = m := by
+ refine ⟨fun h ↦ ?_, ?_⟩
+ · rcases mem_span_set.1 h with ⟨c, cs, rfl⟩
+ have A : c.support ≃ Fin c.support.card := Finset.equivFin _
+ refine ⟨_, fun i ↦ c (A.symm i), fun i ↦ ⟨A.symm i, cs (A.symm i).2⟩, ?_⟩
+ rw [Finsupp.sum, ← Finset.sum_coe_sort c.support]
+ exact Fintype.sum_equiv A.symm _ (fun j ↦ c j • (j : M)) (fun i ↦ rfl)
+ · rintro ⟨n, f, g, rfl⟩
+ exact Submodule.sum_mem _ (fun i _ ↦ Submodule.smul_mem _ _ (Submodule.subset_span (g i).2))
+
+/-- The span of a subset `s` is the union over all `n` of the set of linear combinations of at most
+`n` terms belonging to `s`. -/
+lemma span_eq_iUnion_nat (s : Set M) :
+ (Submodule.span R s : Set M) = ⋃ (n : ℕ),
+ (fun (f : Fin n → (R × M)) ↦ ∑ i, (f i).1 • (f i).2) '' ({f | ∀ i, (f i).2 ∈ s}) := by
+ ext m
+ simp only [SetLike.mem_coe, mem_iUnion, mem_image, mem_setOf_eq, mem_span_set']
+ refine exists_congr (fun n ↦ ⟨?_, ?_⟩)
+ · rintro ⟨f, g, rfl⟩
+ exact ⟨fun i ↦ (f i, g i), fun i ↦ (g i).2, rfl⟩
+ · rintro ⟨f, hf, rfl⟩
+ exact ⟨fun i ↦ (f i).1, fun i ↦ ⟨(f i).2, (hf i)⟩, rfl⟩
+
/-- If `Subsingleton R`, then `M ≃ₗ[R] ι →₀ R` for any type `ι`. -/
@[simps]
def Module.subsingletonEquiv (R M ι : Type*) [Semiring R] [Subsingleton R] [AddCommMonoid M]
@@ -1025,7 +1025,7 @@ theorem finsuppProdLEquiv_apply {α β R M : Type*} [Semiring R] [AddCommMonoid
theorem finsuppProdLEquiv_symm_apply {α β R M : Type*} [Semiring R] [AddCommMonoid M] [Module R M]
(f : α →₀ β →₀ M) (xy) : (finsuppProdLEquiv R).symm f xy = f xy.1 xy.2 := by
conv_rhs =>
- rw [← (finsuppProdLEquiv R).apply_symm_apply f, finsuppProdLEquiv_apply, Prod.mk.eta]
+ rw [← (finsuppProdLEquiv R).apply_symm_apply f, finsuppProdLEquiv_apply]
#align finsupp.finsupp_prod_lequiv_symm_apply Finsupp.finsuppProdLEquiv_symm_apply
end Prod
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -50,7 +50,7 @@ open BigOperators
namespace Finsupp
-variable {α : Type _} {M : Type _} {N : Type _} {P : Type _} {R : Type _} {S : Type _}
+variable {α : Type*} {M : Type*} {N : Type*} {P : Type*} {R : Type*} {S : Type*}
variable [Semiring R] [Semiring S] [AddCommMonoid M] [Module R M]
variable [AddCommMonoid N] [Module R N]
variable [AddCommMonoid P] [Module R P]
@@ -276,7 +276,7 @@ theorem supported_univ : supported M R (Set.univ : Set α) = ⊤ :=
eq_top_iff.2 fun _ _ => Set.subset_univ _
#align finsupp.supported_univ Finsupp.supported_univ
-theorem supported_iUnion {δ : Type _} (s : δ → Set α) :
+theorem supported_iUnion {δ : Type*} (s : δ → Set α) :
supported M R (⋃ i, s i) = ⨆ i, supported M R (s i) := by
refine' le_antisymm _ (iSup_le fun i => supported_mono <| Set.subset_iUnion _ _)
haveI := Classical.decPred fun x => x ∈ ⋃ i, s i
@@ -299,7 +299,7 @@ theorem supported_union (s t : Set α) : supported M R (s ∪ t) = supported M R
by erw [Set.union_eq_iUnion, supported_iUnion, iSup_bool_eq]; rfl
#align finsupp.supported_union Finsupp.supported_union
-theorem supported_iInter {ι : Type _} (s : ι → Set α) :
+theorem supported_iInter {ι : Type*} (s : ι → Set α) :
supported M R (⋂ i, s i) = ⨅ i, supported M R (s i) :=
Submodule.ext fun x => by simp [mem_supported, subset_iInter_iff]
#align finsupp.supported_Inter Finsupp.supported_iInter
@@ -387,7 +387,7 @@ end LSum
section
-variable (M) (R) (X : Type _) (S)
+variable (M) (R) (X : Type*) (S)
variable [Module S M] [SMulCommClass R S M]
/-- A slight rearrangement from `lsum` gives us
@@ -436,7 +436,7 @@ end
section LMapDomain
-variable {α' : Type _} {α'' : Type _} (M R)
+variable {α' : Type*} {α'' : Type*} (M R)
/-- Interpret `Finsupp.mapDomain` as a linear map. -/
def lmapDomain (f : α → α') : (α →₀ M) →ₗ[R] α' →₀ M
@@ -515,7 +515,7 @@ end LMapDomain
section LComapDomain
-variable {β : Type _}
+variable {β : Type*}
/-- Given `f : α → β` and a proof `hf` that `f` is injective, `lcomapDomain f hf` is the linear map
sending `l : β →₀ M` to the finitely supported function from `α` to `M` given by composing
@@ -534,7 +534,7 @@ end LComapDomain
section Total
variable (α) (M) (R)
-variable {α' : Type _} {M' : Type _} [AddCommMonoid M'] [Module R M'] (v : α → M) {v' : α' → M'}
+variable {α' : Type*} {M' : Type*} [AddCommMonoid M'] [Module R M'] (v : α → M) {v' : α' → M'}
/-- Interprets (l : α →₀ R) as linear combination of the elements in the family (v : α → M) and
evaluates this linear combination. -/
@@ -702,7 +702,7 @@ theorem total_option (v : Option α → M) (f : Option α →₀ R) :
by rw [total_apply, sum_option_index_smul, total_apply]; simp
#align finsupp.total_option Finsupp.total_option
-theorem total_total {α β : Type _} (A : α → M) (B : β → α →₀ R) (f : β →₀ R) :
+theorem total_total {α β : Type*} (A : α → M) (B : β → α →₀ R) (f : β →₀ R) :
Finsupp.total α M R A (Finsupp.total β (α →₀ R) R B f) =
Finsupp.total β M R (fun b => Finsupp.total α M R A (B b)) f := by
classical
@@ -769,13 +769,13 @@ end Total
This is `Finsupp.domCongr` as a `LinearEquiv`.
See also `LinearMap.funCongrLeft` for the case of arbitrary functions. -/
-protected def domLCongr {α₁ α₂ : Type _} (e : α₁ ≃ α₂) : (α₁ →₀ M) ≃ₗ[R] α₂ →₀ M :=
+protected def domLCongr {α₁ α₂ : Type*} (e : α₁ ≃ α₂) : (α₁ →₀ M) ≃ₗ[R] α₂ →₀ M :=
(Finsupp.domCongr e : (α₁ →₀ M) ≃+ (α₂ →₀ M)).toLinearEquiv <| by
simpa only [equivMapDomain_eq_mapDomain, domCongr_apply] using (lmapDomain M R e).map_smul
#align finsupp.dom_lcongr Finsupp.domLCongr
@[simp]
-theorem domLCongr_apply {α₁ : Type _} {α₂ : Type _} (e : α₁ ≃ α₂) (v : α₁ →₀ M) :
+theorem domLCongr_apply {α₁ : Type*} {α₂ : Type*} (e : α₁ ≃ α₂) (v : α₁ →₀ M) :
(Finsupp.domLCongr e : _ ≃ₗ[R] _) v = Finsupp.domCongr e v :=
rfl
#align finsupp.dom_lcongr_apply Finsupp.domLCongr_apply
@@ -785,26 +785,26 @@ theorem domLCongr_refl : Finsupp.domLCongr (Equiv.refl α) = LinearEquiv.refl R
LinearEquiv.ext fun _ => equivMapDomain_refl _
#align finsupp.dom_lcongr_refl Finsupp.domLCongr_refl
-theorem domLCongr_trans {α₁ α₂ α₃ : Type _} (f : α₁ ≃ α₂) (f₂ : α₂ ≃ α₃) :
+theorem domLCongr_trans {α₁ α₂ α₃ : Type*} (f : α₁ ≃ α₂) (f₂ : α₂ ≃ α₃) :
(Finsupp.domLCongr f).trans (Finsupp.domLCongr f₂) =
(Finsupp.domLCongr (f.trans f₂) : (_ →₀ M) ≃ₗ[R] _) :=
LinearEquiv.ext fun _ => (equivMapDomain_trans _ _ _).symm
#align finsupp.dom_lcongr_trans Finsupp.domLCongr_trans
@[simp]
-theorem domLCongr_symm {α₁ α₂ : Type _} (f : α₁ ≃ α₂) :
+theorem domLCongr_symm {α₁ α₂ : Type*} (f : α₁ ≃ α₂) :
((Finsupp.domLCongr f).symm : (_ →₀ M) ≃ₗ[R] _) = Finsupp.domLCongr f.symm :=
LinearEquiv.ext fun _ => rfl
#align finsupp.dom_lcongr_symm Finsupp.domLCongr_symm
-- @[simp] -- Porting note: simp can prove this
-theorem domLCongr_single {α₁ : Type _} {α₂ : Type _} (e : α₁ ≃ α₂) (i : α₁) (m : M) :
+theorem domLCongr_single {α₁ : Type*} {α₂ : Type*} (e : α₁ ≃ α₂) (i : α₁) (m : M) :
(Finsupp.domLCongr e : _ ≃ₗ[R] _) (Finsupp.single i m) = Finsupp.single (e i) m := by
simp
#align finsupp.dom_lcongr_single Finsupp.domLCongr_single
/-- An equivalence of sets induces a linear equivalence of `Finsupp`s supported on those sets. -/
-noncomputable def congr {α' : Type _} (s : Set α) (t : Set α') (e : s ≃ t) :
+noncomputable def congr {α' : Type*} (s : Set α) (t : Set α') (e : s ≃ t) :
supported M R s ≃ₗ[R] supported M R t := by
haveI := Classical.decPred fun x => x ∈ s
haveI := Classical.decPred fun x => x ∈ t
@@ -930,7 +930,7 @@ variable (R)
This is the `LinearEquiv` version of `Finsupp.sumFinsuppEquivProdFinsupp`. -/
@[simps apply symm_apply]
-def sumFinsuppLEquivProdFinsupp {α β : Type _} : (Sum α β →₀ M) ≃ₗ[R] (α →₀ M) × (β →₀ M) :=
+def sumFinsuppLEquivProdFinsupp {α β : Type*} : (Sum α β →₀ M) ≃ₗ[R] (α →₀ M) × (β →₀ M) :=
{ sumFinsuppAddEquivProdFinsupp with
map_smul' := by
intros
@@ -943,22 +943,22 @@ def sumFinsuppLEquivProdFinsupp {α β : Type _} : (Sum α β →₀ M) ≃ₗ[R
RingHom.id_apply] }
#align finsupp.sum_finsupp_lequiv_prod_finsupp Finsupp.sumFinsuppLEquivProdFinsupp
-theorem fst_sumFinsuppLEquivProdFinsupp {α β : Type _} (f : Sum α β →₀ M) (x : α) :
+theorem fst_sumFinsuppLEquivProdFinsupp {α β : Type*} (f : Sum α β →₀ M) (x : α) :
(sumFinsuppLEquivProdFinsupp R f).1 x = f (Sum.inl x) :=
rfl
#align finsupp.fst_sum_finsupp_lequiv_prod_finsupp Finsupp.fst_sumFinsuppLEquivProdFinsupp
-theorem snd_sumFinsuppLEquivProdFinsupp {α β : Type _} (f : Sum α β →₀ M) (y : β) :
+theorem snd_sumFinsuppLEquivProdFinsupp {α β : Type*} (f : Sum α β →₀ M) (y : β) :
(sumFinsuppLEquivProdFinsupp R f).2 y = f (Sum.inr y) :=
rfl
#align finsupp.snd_sum_finsupp_lequiv_prod_finsupp Finsupp.snd_sumFinsuppLEquivProdFinsupp
-theorem sumFinsuppLEquivProdFinsupp_symm_inl {α β : Type _} (fg : (α →₀ M) × (β →₀ M)) (x : α) :
+theorem sumFinsuppLEquivProdFinsupp_symm_inl {α β : Type*} (fg : (α →₀ M) × (β →₀ M)) (x : α) :
((sumFinsuppLEquivProdFinsupp R).symm fg) (Sum.inl x) = fg.1 x :=
rfl
#align finsupp.sum_finsupp_lequiv_prod_finsupp_symm_inl Finsupp.sumFinsuppLEquivProdFinsupp_symm_inl
-theorem sumFinsuppLEquivProdFinsupp_symm_inr {α β : Type _} (fg : (α →₀ M) × (β →₀ M)) (y : β) :
+theorem sumFinsuppLEquivProdFinsupp_symm_inr {α β : Type*} (fg : (α →₀ M) × (β →₀ M)) (y : β) :
((sumFinsuppLEquivProdFinsupp R).symm fg) (Sum.inr y) = fg.2 y :=
rfl
#align finsupp.sum_finsupp_lequiv_prod_finsupp_symm_inr Finsupp.sumFinsuppLEquivProdFinsupp_symm_inr
@@ -967,7 +967,7 @@ end Sum
section Sigma
-variable {η : Type _} [Fintype η] {ιs : η → Type _} [Zero α]
+variable {η : Type*} [Fintype η] {ιs : η → Type*} [Zero α]
variable (R)
@@ -975,7 +975,7 @@ variable (R)
`(Σ (j : η), ιs j) →₀ M` and `(j : η) → (ιs j →₀ M)`.
This is the `LinearEquiv` version of `Finsupp.sigmaFinsuppAddEquivPiFinsupp`. -/
-noncomputable def sigmaFinsuppLEquivPiFinsupp {M : Type _} {ιs : η → Type _} [AddCommMonoid M]
+noncomputable def sigmaFinsuppLEquivPiFinsupp {M : Type*} {ιs : η → Type*} [AddCommMonoid M]
[Module R M] : ((Σ j, ιs j) →₀ M) ≃ₗ[R] (j : _) → (ιs j →₀ M) :=
-- Porting note: `ιs` should be specified.
{ sigmaFinsuppAddEquivPiFinsupp (ιs := ιs) with
@@ -985,13 +985,13 @@ noncomputable def sigmaFinsuppLEquivPiFinsupp {M : Type _} {ιs : η → Type _}
#align finsupp.sigma_finsupp_lequiv_pi_finsupp Finsupp.sigmaFinsuppLEquivPiFinsupp
@[simp]
-theorem sigmaFinsuppLEquivPiFinsupp_apply {M : Type _} {ιs : η → Type _} [AddCommMonoid M]
+theorem sigmaFinsuppLEquivPiFinsupp_apply {M : Type*} {ιs : η → Type*} [AddCommMonoid M]
[Module R M] (f : (Σj, ιs j) →₀ M) (j i) : sigmaFinsuppLEquivPiFinsupp R f j i = f ⟨j, i⟩ :=
rfl
#align finsupp.sigma_finsupp_lequiv_pi_finsupp_apply Finsupp.sigmaFinsuppLEquivPiFinsupp_apply
@[simp]
-theorem sigmaFinsuppLEquivPiFinsupp_symm_apply {M : Type _} {ιs : η → Type _} [AddCommMonoid M]
+theorem sigmaFinsuppLEquivPiFinsupp_symm_apply {M : Type*} {ιs : η → Type*} [AddCommMonoid M]
[Module R M] (f : (j : _) → (ιs j →₀ M)) (ji) :
(Finsupp.sigmaFinsuppLEquivPiFinsupp R).symm f ji = f ji.1 ji.2 :=
rfl
@@ -1004,7 +1004,7 @@ section Prod
/-- The linear equivalence between `α × β →₀ M` and `α →₀ β →₀ M`.
This is the `LinearEquiv` version of `Finsupp.finsuppProdEquiv`. -/
-noncomputable def finsuppProdLEquiv {α β : Type _} (R : Type _) {M : Type _} [Semiring R]
+noncomputable def finsuppProdLEquiv {α β : Type*} (R : Type*) {M : Type*} [Semiring R]
[AddCommMonoid M] [Module R M] : (α × β →₀ M) ≃ₗ[R] α →₀ β →₀ M :=
{ finsuppProdEquiv with
map_add' := fun f g => by
@@ -1016,13 +1016,13 @@ noncomputable def finsuppProdLEquiv {α β : Type _} (R : Type _) {M : Type _} [
#align finsupp.finsupp_prod_lequiv Finsupp.finsuppProdLEquiv
@[simp]
-theorem finsuppProdLEquiv_apply {α β R M : Type _} [Semiring R] [AddCommMonoid M] [Module R M]
+theorem finsuppProdLEquiv_apply {α β R M : Type*} [Semiring R] [AddCommMonoid M] [Module R M]
(f : α × β →₀ M) (x y) : finsuppProdLEquiv R f x y = f (x, y) := by
rw [finsuppProdLEquiv, LinearEquiv.coe_mk, finsuppProdEquiv, Finsupp.curry_apply]
#align finsupp.finsupp_prod_lequiv_apply Finsupp.finsuppProdLEquiv_apply
@[simp]
-theorem finsuppProdLEquiv_symm_apply {α β R M : Type _} [Semiring R] [AddCommMonoid M] [Module R M]
+theorem finsuppProdLEquiv_symm_apply {α β R M : Type*} [Semiring R] [AddCommMonoid M] [Module R M]
(f : α →₀ β →₀ M) (xy) : (finsuppProdLEquiv R).symm f xy = f xy.1 xy.2 := by
conv_rhs =>
rw [← (finsuppProdLEquiv R).apply_symm_apply f, finsuppProdLEquiv_apply, Prod.mk.eta]
@@ -1032,7 +1032,7 @@ end Prod
/-- If `R` is countable, then any `R`-submodule spanned by a countable family of vectors is
countable. -/
-instance {ι : Type _} [Countable R] [Countable ι] (v : ι → M) :
+instance {ι : Type*} [Countable R] [Countable ι] (v : ι → M) :
Countable (Submodule.span R (Set.range v)) := by
refine Set.countable_coe_iff.mpr (Set.Countable.mono ?_ (Set.countable_range
(fun c : (ι →₀ R) => c.sum fun i _ => (c i) • v i)))
@@ -1042,9 +1042,9 @@ end Finsupp
section Fintype
-variable {α M : Type _} (R : Type _) [Fintype α] [Semiring R] [AddCommMonoid M] [Module R M]
+variable {α M : Type*} (R : Type*) [Fintype α] [Semiring R] [AddCommMonoid M] [Module R M]
-variable (S : Type _) [Semiring S] [Module S M] [SMulCommClass R S M]
+variable (S : Type*) [Semiring S] [Module S M] [SMulCommClass R S M]
variable (v : α → M)
@@ -1129,7 +1129,7 @@ end SpanRange
end Fintype
-variable {R : Type _} {M : Type _} {N : Type _}
+variable {R : Type*} {M : Type*} {N : Type*}
variable [Semiring R] [AddCommMonoid M] [Module R M] [AddCommMonoid N] [Module R N]
@@ -1153,12 +1153,12 @@ theorem Span.finsupp_total_repr {w : Set M} (x : span R w) :
end
-protected theorem Submodule.finsupp_sum_mem {ι β : Type _} [Zero β] (S : Submodule R M) (f : ι →₀ β)
+protected theorem Submodule.finsupp_sum_mem {ι β : Type*} [Zero β] (S : Submodule R M) (f : ι →₀ β)
(g : ι → β → M) (h : ∀ c, f c ≠ 0 → g c (f c) ∈ S) : f.sum g ∈ S :=
AddSubmonoidClass.finsupp_sum_mem S f g h
#align submodule.finsupp_sum_mem Submodule.finsupp_sum_mem
-theorem LinearMap.map_finsupp_total (f : M →ₗ[R] N) {ι : Type _} {g : ι → M} (l : ι →₀ R) :
+theorem LinearMap.map_finsupp_total (f : M →ₗ[R] N) {ι : Type*} {g : ι → M} (l : ι →₀ R) :
f (Finsupp.total ι M R g l) = Finsupp.total ι N R (f ∘ g) l := by
-- Porting note: `(· ∘ ·)` is required.
simp only [Finsupp.total_apply, Finsupp.total_apply, Finsupp.sum, f.map_sum, f.map_smul, (· ∘ ·)]
@@ -1202,7 +1202,7 @@ theorem mem_span_set {m : M} {s : Set M} :
/-- If `Subsingleton R`, then `M ≃ₗ[R] ι →₀ R` for any type `ι`. -/
@[simps]
-def Module.subsingletonEquiv (R M ι : Type _) [Semiring R] [Subsingleton R] [AddCommMonoid M]
+def Module.subsingletonEquiv (R M ι : Type*) [Semiring R] [Subsingleton R] [AddCommMonoid M]
[Module R M] : M ≃ₗ[R] ι →₀ R where
toFun _ := 0
invFun _ := 0
@@ -1216,7 +1216,7 @@ def Module.subsingletonEquiv (R M ι : Type _) [Semiring R] [Subsingleton R] [Ad
namespace LinearMap
-variable {α : Type _}
+variable {α : Type*}
open Finsupp Function
open Classical
(#6320)
This uncovers a few situations where a lemma was stated with the wrong decidability assumption. The corrected lemmas are strictly more syntactically-general.
This is exhaustive in the LinearAlgebra
folder.
Where removal is impractical, this switches to open Classical in
to make the intent clear.
@@ -46,7 +46,7 @@ function with finite support, module, linear algebra
noncomputable section
open Set LinearMap Submodule
-open Classical BigOperators
+open BigOperators
namespace Finsupp
@@ -180,16 +180,17 @@ theorem span_single_image (s : Set M) (a : α) :
variable (M R)
/-- `Finsupp.supported M R s` is the `R`-submodule of all `p : α →₀ M` such that `p.support ⊆ s`. -/
-def supported (s : Set α) : Submodule R (α →₀ M) := by
- refine' ⟨⟨⟨{ p | ↑p.support ⊆ s }, _⟩, _⟩, _⟩
- · intro p q hp hq
+def supported (s : Set α) : Submodule R (α →₀ M) where
+ carrier := { p | ↑p.support ⊆ s }
+ add_mem' {p q} hp hq := by
+ classical
refine' Subset.trans (Subset.trans (Finset.coe_subset.2 support_add) _) (union_subset hp hq)
rw [Finset.coe_union]
- · simp only [subset_def, Finset.mem_coe, Set.mem_setOf_eq, mem_support_iff, zero_apply]
+ zero_mem' := by
+ simp only [subset_def, Finset.mem_coe, Set.mem_setOf_eq, mem_support_iff, zero_apply]
intro h ha
exact (ha rfl).elim
- · intro a p hp
- refine' Subset.trans (Finset.coe_subset.2 support_smul) hp
+ smul_mem' a p hp := Subset.trans (Finset.coe_subset.2 support_smul) hp
#align finsupp.supported Finsupp.supported
variable {M}
@@ -462,15 +463,17 @@ theorem lmapDomain_comp (f : α → α') (g : α' → α'') :
#align finsupp.lmap_domain_comp Finsupp.lmapDomain_comp
theorem supported_comap_lmapDomain (f : α → α') (s : Set α') :
- supported M R (f ⁻¹' s) ≤ (supported M R s).comap (lmapDomain M R f) :=
- fun l (hl : (l.support : Set α) ⊆ f ⁻¹' s) =>
- show ↑(mapDomain f l).support ⊆ s by
- rw [← Set.image_subset_iff, ← Finset.coe_image] at hl
- exact Set.Subset.trans mapDomain_support hl
+ supported M R (f ⁻¹' s) ≤ (supported M R s).comap (lmapDomain M R f) := by
+ classical
+ intro l (hl : (l.support : Set α) ⊆ f ⁻¹' s)
+ show ↑(mapDomain f l).support ⊆ s
+ rw [← Set.image_subset_iff, ← Finset.coe_image] at hl
+ exact Set.Subset.trans mapDomain_support hl
#align finsupp.supported_comap_lmap_domain Finsupp.supported_comap_lmapDomain
theorem lmapDomain_supported [Nonempty α] (f : α → α') (s : Set α) :
(supported M R s).map (lmapDomain M R f) = supported M R (f '' s) := by
+ classical
inhabit α
refine
le_antisymm
@@ -702,6 +705,7 @@ theorem total_option (v : Option α → M) (f : Option α →₀ R) :
theorem total_total {α β : Type _} (A : α → M) (B : β → α →₀ R) (f : β →₀ R) :
Finsupp.total α M R A (Finsupp.total β (α →₀ R) R B f) =
Finsupp.total β M R (fun b => Finsupp.total α M R A (B b)) f := by
+ classical
simp only [total_apply]
apply induction_linear f
· simp only [sum_zero_index]
@@ -751,6 +755,7 @@ theorem total_comapDomain (f : α → α') (l : α' →₀ R) (hf : Set.InjOn f
theorem total_onFinset {s : Finset α} {f : α → R} (g : α → M) (hf : ∀ a, f a ≠ 0 → a ∈ s) :
Finsupp.total α M R g (Finsupp.onFinset s f hf) = Finset.sum s fun x : α => f x • g x := by
+ classical
simp only [Finsupp.total_apply, Finsupp.sum, Finsupp.onFinset_apply, Finsupp.support_onFinset]
rw [Finset.sum_filter_of_ne]
intro x _ h
@@ -1065,7 +1070,7 @@ theorem Fintype.total_apply (f) : Fintype.total R S v f = ∑ i, f i • v i :=
#align fintype.total_apply Fintype.total_apply
@[simp]
-theorem Fintype.total_apply_single (i : α) (r : R) :
+theorem Fintype.total_apply_single [DecidableEq α] (i : α) (r : R) :
Fintype.total R S v (Pi.single i r) = r • v i := by
simp_rw [Fintype.total_apply, Pi.single_apply, ite_smul, zero_smul]
rw [Finset.sum_ite_eq', if_pos (Finset.mem_univ _)]
@@ -1252,6 +1257,7 @@ def splittingOfFunOnFintypeSurjective [Fintype α] (f : M →ₗ[R] α → R) (s
theorem splittingOfFunOnFintypeSurjective_splits [Fintype α] (f : M →ₗ[R] α → R)
(s : Surjective f) : f.comp (splittingOfFunOnFintypeSurjective f s) = LinearMap.id := by
+ classical
-- Porting note: `ext` can't find appropriate theorems.
refine pi_ext' fun x => ext_ring <| funext fun y => ?_
dsimp [splittingOfFunOnFintypeSurjective]
These declarations broke when I tweaked instances a little bit (in a separate branch that is not ready yet), and I think these declarations can use some extra robustness (usually by providing some extra information explicitly).
@@ -530,8 +530,8 @@ end LComapDomain
section Total
-variable (α) {α' : Type _} (M) {M' : Type _} (R) [Semiring R] [AddCommMonoid M'] [AddCommMonoid M]
- [Module R M'] [Module R M] (v : α → M) {v' : α' → M'}
+variable (α) (M) (R)
+variable {α' : Type _} {M' : Type _} [AddCommMonoid M'] [Module R M'] (v : α → M) {v' : α' → M'}
/-- Interprets (l : α →₀ R) as linear combination of the elements in the family (v : α → M) and
evaluates this linear combination. -/
@@ -3,7 +3,7 @@ Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
-import Mathlib.Data.Finsupp.Defs
+import Mathlib.Data.Finsupp.Encodable
import Mathlib.LinearAlgebra.Pi
import Mathlib.LinearAlgebra.Span
Add the instance:
instance {ι : Type _} [Countable R] [Countable ι] (v : ι → M) : Countable (Submodule.span R (Set.range v))
which is needed to be able to apply Minkowski theorem to ℤ-lattices. This instance, in turn, uses the new instance:
instance [Countable α] [Countable M] : Countable (α →₀ M)
@@ -1025,6 +1025,14 @@ theorem finsuppProdLEquiv_symm_apply {α β R M : Type _} [Semiring R] [AddCommM
end Prod
+/-- If `R` is countable, then any `R`-submodule spanned by a countable family of vectors is
+countable. -/
+instance {ι : Type _} [Countable R] [Countable ι] (v : ι → M) :
+ Countable (Submodule.span R (Set.range v)) := by
+ refine Set.countable_coe_iff.mpr (Set.Countable.mono ?_ (Set.countable_range
+ (fun c : (ι →₀ R) => c.sum fun i _ => (c i) • v i)))
+ exact fun _ h => Finsupp.mem_span_range_iff_exists_finsupp.mp (SetLike.mem_coe.mp h)
+
end Finsupp
section Fintype
@@ -2,16 +2,13 @@
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-
-! This file was ported from Lean 3 source module linear_algebra.finsupp
-! leanprover-community/mathlib commit 9d684a893c52e1d6692a504a118bfccbae04feeb
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Data.Finsupp.Defs
import Mathlib.LinearAlgebra.Pi
import Mathlib.LinearAlgebra.Span
+#align_import linear_algebra.finsupp from "leanprover-community/mathlib"@"9d684a893c52e1d6692a504a118bfccbae04feeb"
+
/-!
# Properties of the module `α →₀ M`
@@ -518,7 +518,7 @@ section LComapDomain
variable {β : Type _}
/-- Given `f : α → β` and a proof `hf` that `f` is injective, `lcomapDomain f hf` is the linear map
-sending `l : β →₀ M` to the finitely supported function from `α` to `M` given by composing
+sending `l : β →₀ M` to the finitely supported function from `α` to `M` given by composing
`l` with `f`.
This is the linear version of `Finsupp.comapDomain`. -/
∑'
precedence (#5615)
∑
, ∏
and variants).([^a-zA-Zα-ωΑ-Ω'𝓝ℳ₀𝕂ₛ)]) \(([∑∏][^()∑∏]*,[^()∑∏:]*)\) ([⊂⊆=<≤])
replaced by $1 $2 $3
@@ -1099,7 +1099,7 @@ variable {v} {x : M}
/-- An element `x` lies in the span of `v` iff it can be written as sum `∑ cᵢ • vᵢ = x`.
-/
theorem mem_span_range_iff_exists_fun :
- x ∈ span R (range v) ↔ ∃ c : α → R, (∑ i, c i • v i) = x := by
+ x ∈ span R (range v) ↔ ∃ c : α → R, ∑ i, c i • v i = x := by
-- Porting note: `Finsupp.equivFunOnFinite.surjective.exists` should be come before `simp`.
rw [Finsupp.equivFunOnFinite.surjective.exists]
simp [Finsupp.mem_span_range_iff_exists_finsupp, Finsupp.equivFunOnFinite_apply]
@@ -1110,7 +1110,7 @@ theorem mem_span_range_iff_exists_fun :
can be written as sum `∑ cᵢ • vᵢ = x`.
-/
theorem top_le_span_range_iff_forall_exists_fun :
- ⊤ ≤ span R (range v) ↔ ∀ x, ∃ c : α → R, (∑ i, c i • v i) = x := by
+ ⊤ ≤ span R (range v) ↔ ∀ x, ∃ c : α → R, ∑ i, c i • v i = x := by
simp_rw [← mem_span_range_iff_exists_fun]
exact ⟨fun h x => h trivial, fun h x _ => h x⟩
#align top_le_span_range_iff_forall_exists_fun top_le_span_range_iff_forall_exists_fun
@@ -1171,7 +1171,7 @@ theorem Submodule.mem_iSup_iff_exists_finset {ι : Sort _} {p : ι → Submodule
#align submodule.mem_supr_iff_exists_finset Submodule.mem_iSup_iff_exists_finset
theorem mem_span_finset {s : Finset M} {x : M} :
- x ∈ span R (↑s : Set M) ↔ ∃ f : M → R, (∑ i in s, f i • i) = x :=
+ x ∈ span R (↑s : Set M) ↔ ∃ f : M → R, ∑ i in s, f i • i = x :=
⟨fun hx =>
let ⟨v, hvs, hvx⟩ :=
(Finsupp.mem_span_image_iff_total _).1
@@ -134,7 +134,7 @@ theorem ker_lsingle (a : α) : ker (lsingle a : M →ₗ[R] α →₀ M) = ⊥ :
#align finsupp.ker_lsingle Finsupp.ker_lsingle
theorem lsingle_range_le_ker_lapply (s t : Set α) (h : Disjoint s t) :
- (⨆ a ∈ s, LinearMap.range (lsingle a : M →ₗ[R] α →₀ M)) ≤
+ ⨆ a ∈ s, LinearMap.range (lsingle a : M →ₗ[R] α →₀ M) ≤
⨅ a ∈ t, ker (lapply a : (α →₀ M) →ₗ[R] M) := by
refine' iSup_le fun a₁ => iSup_le fun h₁ => range_le_iff_comap.2 _
simp only [(ker_comp _ _).symm, eq_top_iff, SetLike.le_def, mem_ker, comap_iInf, mem_iInf]
@@ -143,12 +143,12 @@ theorem lsingle_range_le_ker_lapply (s t : Set α) (h : Disjoint s t) :
exact single_eq_of_ne this
#align finsupp.lsingle_range_le_ker_lapply Finsupp.lsingle_range_le_ker_lapply
-theorem iInf_ker_lapply_le_bot : (⨅ a, ker (lapply a : (α →₀ M) →ₗ[R] M)) ≤ ⊥ := by
+theorem iInf_ker_lapply_le_bot : ⨅ a, ker (lapply a : (α →₀ M) →ₗ[R] M) ≤ ⊥ := by
simp only [SetLike.le_def, mem_iInf, mem_ker, mem_bot, lapply_apply]
exact fun a h => Finsupp.ext h
#align finsupp.infi_ker_lapply_le_bot Finsupp.iInf_ker_lapply_le_bot
-theorem iSup_lsingle_range : (⨆ a, LinearMap.range (lsingle a : M →ₗ[R] α →₀ M)) = ⊤ := by
+theorem iSup_lsingle_range : ⨆ a, LinearMap.range (lsingle a : M →ₗ[R] α →₀ M) = ⊤ := by
refine' eq_top_iff.2 <| SetLike.le_def.2 fun f _ => _
rw [← sum_single f]
exact sum_mem fun a _ => Submodule.mem_iSup_of_mem a ⟨_, rfl⟩
@@ -160,8 +160,8 @@ theorem disjoint_lsingle_lsingle (s t : Set α) (hs : Disjoint s t) :
-- Porting note: 2 placeholders are added to prevent timeout.
refine'
(Disjoint.mono
- (lsingle_range_le_ker_lapply s (sᶜ) _)
- (lsingle_range_le_ker_lapply t (tᶜ) _))
+ (lsingle_range_le_ker_lapply s sᶜ _)
+ (lsingle_range_le_ker_lapply t tᶜ _))
_
· apply disjoint_compl_right
· apply disjoint_compl_right
ext
(#5258)
Co-authored-by: Xavier Roblot <46200072+xroblot@users.noreply.github.com> Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr> Co-authored-by: Riccardo Brasca <riccardo.brasca@gmail.com> Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Pol'tta / Miyahara Kō <pol_tta@outlook.jp> Co-authored-by: Jason Yuen <jason_yuen2007@hotmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: Jireh Loreaux <loreaujy@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Heather Macbeth <25316162+hrmacbeth@users.noreply.github.com> Co-authored-by: Jujian Zhang <jujian.zhang1998@outlook.com> Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>
@@ -254,7 +254,7 @@ end
theorem restrictDom_comp_subtype (s : Set α) :
(restrictDom M R s).comp (Submodule.subtype _) = LinearMap.id := by
- ext (l a)
+ ext l a
by_cases h : a ∈ s <;> simp [h]
exact ((mem_supported' R l.1).1 l.2 a h).symm
#align finsupp.restrict_dom_comp_subtype Finsupp.restrictDom_comp_subtype
@@ -1187,8 +1187,6 @@ theorem mem_span_set {m : M} {s : Set M} :
m ∈ Submodule.span R s ↔
∃ c : M →₀ R, (c.support : Set M) ⊆ s ∧ (c.sum fun mi r => r • mi) = m := by
conv_lhs => rw [← Set.image_id s]
- -- Porting note: `simp_rw [← exists_prop]` is not necessary because of the
- -- new definition of `∃ x, p x`.
exact Finsupp.mem_span_image_iff_total R (v := _root_.id (α := M))
#align mem_span_set mem_span_set
I wrote a script to find lines that contain an odd number of backticks
@@ -37,8 +37,8 @@ interpreted as a submodule of `α →₀ M`. We also define `LinearMap` versions
* `Finsupp.domLCongr`: a `LinearEquiv` version of `Finsupp.domCongr`;
* `Finsupp.congr`: if the sets `s` and `t` are equivalent, then `supported M R s` is equivalent to
`supported M R t`;
-* `Finsupp.lcongr`: a `LinearEquiv`alence between `α →₀ M` and `β →₀ N` constructed using `e : α ≃
- β` and `e' : M ≃ₗ[R] N`.
+* `Finsupp.lcongr`: a `LinearEquiv`alence between `α →₀ M` and `β →₀ N` constructed using
+ `e : α ≃ β` and `e' : M ≃ₗ[R] N`.
## Tags
@@ -22,7 +22,7 @@ In this file we define `Finsupp.supported s` to be the set `{f : α →₀ M | f
interpreted as a submodule of `α →₀ M`. We also define `LinearMap` versions of various maps:
* `Finsupp.lsingle a : M →ₗ[R] ι →₀ M`: `Finsupp.single a` as a linear map;
-* `Finsupp.lapply a : (ι →₀ M) →ₗ[R] M`: the map `λ f, f a` as a linear map;
+* `Finsupp.lapply a : (ι →₀ M) →ₗ[R] M`: the map `fun f ↦ f a` as a linear map;
* `Finsupp.lsubtypeDomain (s : Set α) : (α →₀ M) →ₗ[R] (s →₀ M)`: restriction to a subtype as a
linear map;
* `Finsupp.restrictDom`: `Finsupp.filter` as a linear map to `Finsupp.supported s`;
Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Alex J Best <alex.j.best@gmail.com>
@@ -1047,19 +1047,10 @@ See note [bundled maps over different rings] for why separate `R` and `S` semiri
protected def Fintype.total : (α → M) →ₗ[S] (α → R) →ₗ[R] M where
toFun v :=
{ toFun := fun f => ∑ i, f i • v i
- map_add' := fun f g => by
- simp_rw [← Finset.sum_add_distrib, ← add_smul]
- rfl
- map_smul' := fun r f => by
- simp_rw [Finset.smul_sum, smul_smul]
- rfl }
- map_add' u v := by
- ext
- simp [Finset.sum_add_distrib, Pi.add_apply, smul_add]
- map_smul' r v := by
- ext g
- -- Porting note: `smul_comm _ r` → `fun x => smul_comm (g x) r (v x)`
- simp [Finset.smul_sum, fun x => smul_comm (g x) r (v x)]
+ map_add' := fun f g => by simp_rw [← Finset.sum_add_distrib, ← add_smul]; rfl
+ map_smul' := fun r f => by simp_rw [Finset.smul_sum, smul_smul]; rfl }
+ map_add' u v := by ext; simp [Finset.sum_add_distrib, Pi.add_apply, smul_add]
+ map_smul' r v := by ext; simp [Finset.smul_sum, smul_comm]
#align fintype.total Fintype.total
variable {S}
fix-comments.py
on all files.@@ -23,7 +23,7 @@ interpreted as a submodule of `α →₀ M`. We also define `LinearMap` versions
* `Finsupp.lsingle a : M →ₗ[R] ι →₀ M`: `Finsupp.single a` as a linear map;
* `Finsupp.lapply a : (ι →₀ M) →ₗ[R] M`: the map `λ f, f a` as a linear map;
-* `Finsupp.lsubtypeDomain (s : set α) : (α →₀ M) →ₗ[R] (s →₀ M)`: restriction to a subtype as a
+* `Finsupp.lsubtypeDomain (s : Set α) : (α →₀ M) →ₗ[R] (s →₀ M)`: restriction to a subtype as a
linear map;
* `Finsupp.restrictDom`: `Finsupp.filter` as a linear map to `Finsupp.supported s`;
* `Finsupp.lsum`: `Finsupp.sum` or `Finsupp.liftAddHom` as a `LinearMap`;
@@ -724,7 +724,7 @@ variable (α) (M) (v)
/-- `Finsupp.totalOn M v s` interprets `p : α →₀ R` as a linear combination of a
subset of the vectors in `v`, mapping it to the span of those vectors.
-The subset is indicated by a set `s : set α` of indices.
+The subset is indicated by a set `s : Set α` of indices.
-/
protected def totalOn (s : Set α) : supported R R s →ₗ[R] span R (v '' s) :=
LinearMap.codRestrict _ ((Finsupp.total _ _ _ v).comp (Submodule.subtype (supported R R s)))
sSup
/iSup
(#3938)
As discussed on Zulip
supₛ
→ sSup
infₛ
→ sInf
supᵢ
→ iSup
infᵢ
→ iInf
bsupₛ
→ bsSup
binfₛ
→ bsInf
bsupᵢ
→ biSup
binfᵢ
→ biInf
csupₛ
→ csSup
cinfₛ
→ csInf
csupᵢ
→ ciSup
cinfᵢ
→ ciInf
unionₛ
→ sUnion
interₛ
→ sInter
unionᵢ
→ iUnion
interᵢ
→ iInter
bunionₛ
→ bsUnion
binterₛ
→ bsInter
bunionᵢ
→ biUnion
binterᵢ
→ biInter
Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>
@@ -136,23 +136,23 @@ theorem ker_lsingle (a : α) : ker (lsingle a : M →ₗ[R] α →₀ M) = ⊥ :
theorem lsingle_range_le_ker_lapply (s t : Set α) (h : Disjoint s t) :
(⨆ a ∈ s, LinearMap.range (lsingle a : M →ₗ[R] α →₀ M)) ≤
⨅ a ∈ t, ker (lapply a : (α →₀ M) →ₗ[R] M) := by
- refine' supᵢ_le fun a₁ => supᵢ_le fun h₁ => range_le_iff_comap.2 _
- simp only [(ker_comp _ _).symm, eq_top_iff, SetLike.le_def, mem_ker, comap_infᵢ, mem_infᵢ]
+ refine' iSup_le fun a₁ => iSup_le fun h₁ => range_le_iff_comap.2 _
+ simp only [(ker_comp _ _).symm, eq_top_iff, SetLike.le_def, mem_ker, comap_iInf, mem_iInf]
intro b _ a₂ h₂
have : a₁ ≠ a₂ := fun eq => h.le_bot ⟨h₁, eq.symm ▸ h₂⟩
exact single_eq_of_ne this
#align finsupp.lsingle_range_le_ker_lapply Finsupp.lsingle_range_le_ker_lapply
-theorem infᵢ_ker_lapply_le_bot : (⨅ a, ker (lapply a : (α →₀ M) →ₗ[R] M)) ≤ ⊥ := by
- simp only [SetLike.le_def, mem_infᵢ, mem_ker, mem_bot, lapply_apply]
+theorem iInf_ker_lapply_le_bot : (⨅ a, ker (lapply a : (α →₀ M) →ₗ[R] M)) ≤ ⊥ := by
+ simp only [SetLike.le_def, mem_iInf, mem_ker, mem_bot, lapply_apply]
exact fun a h => Finsupp.ext h
-#align finsupp.infi_ker_lapply_le_bot Finsupp.infᵢ_ker_lapply_le_bot
+#align finsupp.infi_ker_lapply_le_bot Finsupp.iInf_ker_lapply_le_bot
-theorem supᵢ_lsingle_range : (⨆ a, LinearMap.range (lsingle a : M →ₗ[R] α →₀ M)) = ⊤ := by
+theorem iSup_lsingle_range : (⨆ a, LinearMap.range (lsingle a : M →ₗ[R] α →₀ M)) = ⊤ := by
refine' eq_top_iff.2 <| SetLike.le_def.2 fun f _ => _
rw [← sum_single f]
- exact sum_mem fun a _ => Submodule.mem_supᵢ_of_mem a ⟨_, rfl⟩
-#align finsupp.supr_lsingle_range Finsupp.supᵢ_lsingle_range
+ exact sum_mem fun a _ => Submodule.mem_iSup_of_mem a ⟨_, rfl⟩
+#align finsupp.supr_lsingle_range Finsupp.iSup_lsingle_range
theorem disjoint_lsingle_lsingle (s t : Set α) (hs : Disjoint s t) :
Disjoint (⨆ a ∈ s, LinearMap.range (lsingle a : M →ₗ[R] α →₀ M))
@@ -166,13 +166,13 @@ theorem disjoint_lsingle_lsingle (s t : Set α) (hs : Disjoint s t) :
· apply disjoint_compl_right
· apply disjoint_compl_right
rw [disjoint_iff_inf_le]
- refine' le_trans (le_infᵢ fun i => _) infᵢ_ker_lapply_le_bot
+ refine' le_trans (le_iInf fun i => _) iInf_ker_lapply_le_bot
classical
by_cases his : i ∈ s
· by_cases hit : i ∈ t
· exact (hs.le_bot ⟨his, hit⟩).elim
- exact inf_le_of_right_le (infᵢ_le_of_le i <| infᵢ_le _ hit)
- exact inf_le_of_left_le (infᵢ_le_of_le i <| infᵢ_le _ his)
+ exact inf_le_of_right_le (iInf_le_of_le i <| iInf_le _ hit)
+ exact inf_le_of_left_le (iInf_le_of_le i <| iInf_le _ his)
#align finsupp.disjoint_lsingle_lsingle Finsupp.disjoint_lsingle_lsingle
theorem span_single_image (s : Set M) (a : α) :
@@ -278,9 +278,9 @@ theorem supported_univ : supported M R (Set.univ : Set α) = ⊤ :=
eq_top_iff.2 fun _ _ => Set.subset_univ _
#align finsupp.supported_univ Finsupp.supported_univ
-theorem supported_unionᵢ {δ : Type _} (s : δ → Set α) :
+theorem supported_iUnion {δ : Type _} (s : δ → Set α) :
supported M R (⋃ i, s i) = ⨆ i, supported M R (s i) := by
- refine' le_antisymm _ (supᵢ_le fun i => supported_mono <| Set.subset_unionᵢ _ _)
+ refine' le_antisymm _ (iSup_le fun i => supported_mono <| Set.subset_iUnion _ _)
haveI := Classical.decPred fun x => x ∈ ⋃ i, s i
suffices
LinearMap.range ((Submodule.subtype _).comp (restrictDom M R (⋃ i, s i))) ≤
@@ -294,20 +294,20 @@ theorem supported_unionᵢ {δ : Type _} (s : δ → Set α) :
· refine' fun x a l _ _ => add_mem _
by_cases h : ∃ i, x ∈ s i <;> simp [h]
· cases' h with i hi
- exact le_supᵢ (fun i => supported M R (s i)) i (single_mem_supported R _ hi)
-#align finsupp.supported_Union Finsupp.supported_unionᵢ
+ exact le_iSup (fun i => supported M R (s i)) i (single_mem_supported R _ hi)
+#align finsupp.supported_Union Finsupp.supported_iUnion
theorem supported_union (s t : Set α) : supported M R (s ∪ t) = supported M R s ⊔ supported M R t :=
- by erw [Set.union_eq_unionᵢ, supported_unionᵢ, supᵢ_bool_eq]; rfl
+ by erw [Set.union_eq_iUnion, supported_iUnion, iSup_bool_eq]; rfl
#align finsupp.supported_union Finsupp.supported_union
-theorem supported_interᵢ {ι : Type _} (s : ι → Set α) :
+theorem supported_iInter {ι : Type _} (s : ι → Set α) :
supported M R (⋂ i, s i) = ⨅ i, supported M R (s i) :=
- Submodule.ext fun x => by simp [mem_supported, subset_interᵢ_iff]
-#align finsupp.supported_Inter Finsupp.supported_interᵢ
+ Submodule.ext fun x => by simp [mem_supported, subset_iInter_iff]
+#align finsupp.supported_Inter Finsupp.supported_iInter
theorem supported_inter (s t : Set α) : supported M R (s ∩ t) = supported M R s ⊓ supported M R t :=
- by rw [Set.inter_eq_interᵢ, supported_interᵢ, infᵢ_bool_eq]; rfl
+ by rw [Set.inter_eq_iInter, supported_iInter, iInf_bool_eq]; rfl
#align finsupp.supported_inter Finsupp.supported_inter
theorem disjoint_supported_supported {s t : Set α} (h : Disjoint s t) :
@@ -1163,21 +1163,21 @@ theorem LinearMap.map_finsupp_total (f : M →ₗ[R] N) {ι : Type _} {g : ι
simp only [Finsupp.total_apply, Finsupp.total_apply, Finsupp.sum, f.map_sum, f.map_smul, (· ∘ ·)]
#align linear_map.map_finsupp_total LinearMap.map_finsupp_total
-theorem Submodule.exists_finset_of_mem_supᵢ {ι : Sort _} (p : ι → Submodule R M) {m : M}
+theorem Submodule.exists_finset_of_mem_iSup {ι : Sort _} (p : ι → Submodule R M) {m : M}
(hm : m ∈ ⨆ i, p i) : ∃ s : Finset ι, m ∈ ⨆ i ∈ s, p i := by
have :=
- CompleteLattice.IsCompactElement.exists_finset_of_le_supᵢ (Submodule R M)
+ CompleteLattice.IsCompactElement.exists_finset_of_le_iSup (Submodule R M)
(Submodule.singleton_span_isCompactElement m) p
simp only [Submodule.span_singleton_le_iff_mem] at this
exact this hm
-#align submodule.exists_finset_of_mem_supr Submodule.exists_finset_of_mem_supᵢ
+#align submodule.exists_finset_of_mem_supr Submodule.exists_finset_of_mem_iSup
-/-- `Submodule.exists_finset_of_mem_supᵢ` as an `iff` -/
-theorem Submodule.mem_supᵢ_iff_exists_finset {ι : Sort _} {p : ι → Submodule R M} {m : M} :
+/-- `Submodule.exists_finset_of_mem_iSup` as an `iff` -/
+theorem Submodule.mem_iSup_iff_exists_finset {ι : Sort _} {p : ι → Submodule R M} {m : M} :
(m ∈ ⨆ i, p i) ↔ ∃ s : Finset ι, m ∈ ⨆ i ∈ s, p i :=
- ⟨Submodule.exists_finset_of_mem_supᵢ p, fun ⟨_, hs⟩ =>
- supᵢ_mono (fun i => (supᵢ_const_le : _ ≤ p i)) hs⟩
-#align submodule.mem_supr_iff_exists_finset Submodule.mem_supᵢ_iff_exists_finset
+ ⟨Submodule.exists_finset_of_mem_iSup p, fun ⟨_, hs⟩ =>
+ iSup_mono (fun i => (iSup_const_le : _ ≤ p i)) hs⟩
+#align submodule.mem_supr_iff_exists_finset Submodule.mem_iSup_iff_exists_finset
theorem mem_span_finset {s : Finset M} {x : M} :
x ∈ span R (↑s : Set M) ↔ ∃ f : M → R, (∑ i in s, f i • i) = x :=
by
s! (#3825)
This PR puts, with one exception, every single remaining by
that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh
. The exception is when the by
begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.
Essentially this is s/\n *by$/ by/g
, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated by
s".
@@ -499,8 +499,7 @@ theorem lmapDomain_disjoint_ker (f : α → α') {s : Set α}
simp; ext x
haveI := Classical.decPred fun x => x ∈ s
by_cases xs : x ∈ s
- · have : Finsupp.sum l (fun a => Finsupp.single (f a)) (f x) = 0 :=
- by
+ · have : Finsupp.sum l (fun a => Finsupp.single (f a)) (f x) = 0 := by
rw [h₂]
rfl
rw [Finsupp.sum_apply, Finsupp.sum, Finset.sum_eq_single x, single_eq_same] at this
@@ -1078,9 +1077,8 @@ theorem Fintype.total_apply_single (i : α) (r : R) :
variable (S)
-theorem Finsupp.total_eq_fintype_total_apply (x : α → R) :
- Finsupp.total α M R v ((Finsupp.linearEquivFunOnFinite R R α).symm x) = Fintype.total R S v x :=
- by
+theorem Finsupp.total_eq_fintype_total_apply (x : α → R) : Finsupp.total α M R v
+ ((Finsupp.linearEquivFunOnFinite R R α).symm x) = Fintype.total R S v x := by
apply Finset.sum_subset
· exact Finset.subset_univ _
· intro x _ hx
finset
lemmas around (#3748)
Match https://github.com/leanprover-community/mathlib/pull/18900
Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
! This file was ported from Lean 3 source module linear_algebra.finsupp
-! leanprover-community/mathlib commit 3dec44d0b621a174c56e994da4aae15ba60110a2
+! leanprover-community/mathlib commit 9d684a893c52e1d6692a504a118bfccbae04feeb
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -285,7 +285,7 @@ theorem supported_unionᵢ {δ : Type _} (s : δ → Set α) :
suffices
LinearMap.range ((Submodule.subtype _).comp (restrictDom M R (⋃ i, s i))) ≤
⨆ i, supported M R (s i) by
- rwa [LinearMap.range_comp, range_restrictDom, map_top, range_subtype] at this
+ rwa [LinearMap.range_comp, range_restrictDom, Submodule.map_top, range_subtype] at this
rw [range_le_iff_comap, eq_top_iff]
rintro l ⟨⟩
-- Porting note: Was ported as `induction l using Finsupp.induction`
@@ -735,8 +735,9 @@ protected def totalOn (s : Set α) : supported R R s →ₗ[R] span R (v '' s) :
variable {α} {M} {v}
theorem totalOn_range (s : Set α) : LinearMap.range (Finsupp.totalOn α M R v s) = ⊤ := by
- rw [Finsupp.totalOn, LinearMap.range_eq_map, LinearMap.map_codRestrict, ←
- LinearMap.range_le_iff_comap, range_subtype, map_top, LinearMap.range_comp, range_subtype]
+ rw [Finsupp.totalOn, LinearMap.range_eq_map, LinearMap.map_codRestrict,
+ ←LinearMap.range_le_iff_comap, range_subtype, Submodule.map_top, LinearMap.range_comp,
+ range_subtype]
exact (span_image_eq_map_total _ _).le
#align finsupp.total_on_range Finsupp.totalOn_range
@@ -1137,11 +1137,6 @@ section
variable (R)
--- Porting note: `irreducible_def` produces a structure.
--- When a structure is defined, an injectivity theorem of the constructor is
--- generated, which has `simp` attr, but this get a `simpNF` linter.
--- So, this option is required.
-set_option genInjectivity false in
/-- Pick some representation of `x : span R w` as a linear combination in `w`,
using the axiom of choice.
-/
@@ -578,6 +578,10 @@ theorem apply_total (f : M →ₗ[R] M') (v) (l : α →₀ R) :
apply Finsupp.induction_linear l <;> simp (config := { contextual := true })
#align finsupp.apply_total Finsupp.apply_total
+theorem apply_total_id (f : M →ₗ[R] M') (l : M →₀ R) :
+ f (Finsupp.total M M R _root_.id l) = Finsupp.total M M' R f l :=
+ apply_total ..
+
theorem total_unique [Unique α] (l : α →₀ R) (v) :
Finsupp.total α M R v l = l default • v default := by rw [← total_single, ← unique_single l]
#align finsupp.total_unique Finsupp.total_unique
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
! This file was ported from Lean 3 source module linear_algebra.finsupp
-! leanprover-community/mathlib commit dc6c365e751e34d100e80fe6e314c3c3e0fd2988
+! leanprover-community/mathlib commit 3dec44d0b621a174c56e994da4aae15ba60110a2
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -389,7 +389,8 @@ end LSum
section
-variable (M) (R) (X : Type _)
+variable (M) (R) (X : Type _) (S)
+variable [Module S M] [SMulCommClass R S M]
/-- A slight rearrangement from `lsum` gives us
the bijection underlying the free-forgetful adjunction for R-modules.
@@ -409,6 +410,30 @@ theorem lift_apply (f) (g) : ((lift M R X) f) g = g.sum fun x r => r • f x :=
rfl
#align finsupp.lift_apply Finsupp.lift_apply
+/-- Given compatible `S` and `R`-module structures on `M` and a type `X`, the set of functions
+`X → M` is `S`-linearly equivalent to the `R`-linear maps from the free `R`-module
+on `X` to `M`. -/
+noncomputable def llift : (X → M) ≃ₗ[S] (X →₀ R) →ₗ[R] M :=
+ { lift M R X with
+ map_smul' := by
+ intros
+ dsimp
+ ext
+ simp only [coe_comp, Function.comp_apply, lsingle_apply, lift_apply, Pi.smul_apply,
+ sum_single_index, zero_smul, one_smul, LinearMap.smul_apply] }
+#align finsupp.llift Finsupp.llift
+
+@[simp]
+theorem llift_apply (f : X → M) (x : X →₀ R) : llift M R S X f x = lift M R X f x :=
+ rfl
+#align finsupp.llift_apply Finsupp.llift_apply
+
+@[simp]
+theorem llift_symm_apply (f : (X →₀ R) →ₗ[R] M) (x : X) :
+ (llift M R S X).symm f x = f (single x 1) :=
+ rfl
+#align finsupp.llift_symm_apply Finsupp.llift_symm_apply
+
end
section LMapDomain
These lemmas are not tautologies, despite the assumption that they were. We know this because otherwise CI would fail.
After adding these back, a few statements downstream need to change from statements about toEquiv
to statements about EquivLike.toEquiv
.
@@ -905,8 +905,8 @@ def sumFinsuppLEquivProdFinsupp {α β : Type _} : (Sum α β →₀ M) ≃ₗ[R
intros
ext <;>
-- Porting note: `add_equiv.to_fun_eq_coe` →
- -- `Equiv.toFun_as_coe` & `AddEquiv.coe_toEquiv`
- simp only [Equiv.toFun_as_coe, AddEquiv.coe_toEquiv, Prod.smul_fst,
+ -- `Equiv.toFun_as_coe` & `AddEquiv.toEquiv_eq_coe` & `AddEquiv.coe_toEquiv`
+ simp only [Equiv.toFun_as_coe, AddEquiv.toEquiv_eq_coe, AddEquiv.coe_toEquiv, Prod.smul_fst,
Prod.smul_snd, smul_apply,
snd_sumFinsuppAddEquivProdFinsupp, fst_sumFinsuppAddEquivProdFinsupp,
RingHom.id_apply] }
@@ -255,7 +255,7 @@ end
theorem restrictDom_comp_subtype (s : Set α) :
(restrictDom M R s).comp (Submodule.subtype _) = LinearMap.id := by
ext (l a)
- by_cases a ∈ s <;> simp [h]
+ by_cases h : a ∈ s <;> simp [h]
exact ((mem_supported' R l.1).1 l.2 a h).symm
#align finsupp.restrict_dom_comp_subtype Finsupp.restrictDom_comp_subtype
@@ -292,7 +292,7 @@ theorem supported_unionᵢ {δ : Type _} (s : δ → Set α) :
refine Finsupp.induction l ?_ ?_
· exact zero_mem _
· refine' fun x a l _ _ => add_mem _
- by_cases ∃ i, x ∈ s i <;> simp [h]
+ by_cases h : ∃ i, x ∈ s i <;> simp [h]
· cases' h with i hi
exact le_supᵢ (fun i => supported M R (s i)) i (single_mem_supported R _ hi)
#align finsupp.supported_Union Finsupp.supported_unionᵢ
@@ -653,7 +653,7 @@ theorem span_image_eq_map_total (s : Set α) :
have : ∀ i, z i • v i ∈ span R (v '' s) := by
intro c
haveI := Classical.decPred fun x => x ∈ s
- by_cases c ∈ s
+ by_cases h : c ∈ s
· exact smul_mem _ _ (subset_span (Set.mem_image_of_mem _ h))
· simp [(Finsupp.mem_supported' R _).1 hz _ h]
-- Porting note: `rw` is required to infer metavariables in `sum_mem`.
@@ -898,7 +898,7 @@ variable (R)
/-- The linear equivalence between `(α ⊕ β) →₀ M` and `(α →₀ M) × (β →₀ M)`.
This is the `LinearEquiv` version of `Finsupp.sumFinsuppEquivProdFinsupp`. -/
-@[simps apply symmApply]
+@[simps apply symm_apply]
def sumFinsuppLEquivProdFinsupp {α β : Type _} : (Sum α β →₀ M) ≃ₗ[R] (α →₀ M) × (β →₀ M) :=
{ sumFinsuppAddEquivProdFinsupp with
map_smul' := by
The unported dependencies are